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B LIBIiARY OF COXGIIKSS. I 



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| UNITED STATES OF AMERICA. 9 



?^??-:^?-:-'':^v 



FARM IMPLEMENTS, 



PRINCIPLES OF THEIR CONSTRUCTION AND USE; 



ELEMENTARY AND FAMILIAR TREATISE 



ON MECHANICS, 



AND ON NATURAL PHILOSOPHY GENERALLY, AS APPLIED 

TO THE ORDINARY PRACTICES OF 

AGRICULTURE. 



WITH 200 ENGRAVED ILLUSTRATIONS 



BY JOHN J. THOMAS. 



" We should like to see this work printed, bound, and hung up in every work- 
shop, tool-room, and farmer's book-shelf in the country. It gives the reason and 
explains the action of mechanical powers, and the forces of nature generally, with 
illustrations so directly drawn from the farmer's daily routine, that it gives a direct 
meaning and value to every point, rarely found in text-books." — Downing's Preview 
of the First Edition. 




NEW YORK: 

HARPER & BROTHERS, PUBLISHERS, 

82 BEEKMAN STREET. 

1854. 



Entered, according to Act of Congress, in the year 1854, by 

HARPER & BROTHERS, 
In tlic Clerk's Office for the Southern District of New York. 



PREFACE, 



This work, in its original form, was published in the 
Transactions of the New York State Agricultural So- 
ciety for 1850, under the title of-" Agricultural Dy- 
namics," or the Science of Farm Forces. The present 
edition is prepared on the basis of the original essay, 
and is thoroughly revised and greatly enlarged, with 
the addition of more than double the former number 
of illustrations. 

It comprehends those branches of Natural Philoso- 
phy known as Mechanics, Hydrodynamics, Pneumat- 
ics, and Heat, in their more common application to the 
practices of modern improved farming ; and, so far as 
practicable, technical words and phrases have been 
avoided, and the whole rendered simple and intelligi- 
ble to ordinary readers. 

The leading principles have been derived from the 
existing stock of knowledge ; but no treatise on these 
subjects, as specially applied to agriculture, having be- 
fore appeared, the various examples of the application 
of those principles to the structure and use of farm im- 
plements, and to the farmer's daily routine, are mostly 
original. 

For the purpose of adapting the work to schools, 
wherever it may be desirable, it is divided into sec- 
tions, each of sufficient length for a single recitation. 



CONTENTS. 

PART I. 

MECHANICS. 
CHAPTER I. 

INTRODUCTION. 

Page 

Benefits of Mechanical Knowledge 13 

CHAPTER II. 

GENERAL PRINCIPLES OF MECHANICS. 

SECTION I. 

General Properties of Matter 18 

Divisibility 18 

Impenetrability 20 

Indestructibility 20 

Inertia 21 

SECTION II. 

Momentum, or Inertia of moving Bodies 24 

The Fly-wheel : 27 

Application of Fly-wheel in churning and cutting Straw 28 

Estimating the Quantity of Momentum 30 

SECTION III. 

Compound Motion 31 

Centrifugal Force *..... 34 

CHAPTER III. 

ATTRACTION. 
SECTION I. 

Gravitation 35 

Measuring Velocity of falling Bodies — Atwood's Machine 38 



Vlll CONTENTS. 

SECTION II. 

Page 

Cohesion 42 

Strength of Materials 43 

Capillary Attraction 47 

Ascent of Sap 49 

SECTION III. 

Centre of Gravity 50 

Line of Direction 52 

CHAPTER IV. 

SIMPLE MACHINES, OR MECHANICAL POWERS. 

SECTION I. 

Advantages of Machines 60 

Law of Virtual Velocities 61 

SECTION II. 
The Lever 63 

SECTION III. 

Estimating the Power of Levers 67 

Combination of Levers 70 

Weighing Machine 71 

Machines for extracting Stumps 72 

SECTION IV. 

"Wheel and Axle 75 

Mole-plow 78 

Band and Cog Wheels 79 

Form of Teeth or Cogs 80 

SECTION V. 
The Pulley 83 

SECTION VI. 

The Inclined Plane 86 

Ascent in Roads 87 

Form and Materials for Roads 90 

Importance of good Roads 92 

SECTION VII. 

The Wedge 93 

The Screw 94 



CONTENTS. IX 



CHAPTER V. 

APPLICATION OF MECHANICAL PRINCIPLES IN THE STRUCTURE OP THE 
PARTS OP IMPLEMENTS AND MACHINES Page 96 

CHAPTER VI. 

FRICTION. 

SECTION L 

Rolling Friction 103 

Nature of Friction 104 

Estimating the Amount of Friction 104 

SECTION II. 

Results with the Dynamometer 107 

Width of Wheels 109 

Velocity as affecting Friction 110 

Friction at the Axle Ill 

Friction Wheels 112 

SECTION III. 

Lubricating Substances 113 

Advantages of Friction 115 

SECTION IV. 

Principles of Draught 117 

Combined Draught of Animals 120 

SECTION V. 

Construction and use of the Dynamometer 122 

Self-recording Dynamometer , 125 

Dynamometer for Rotary Motion 126 

CHAPTER VII. 

CONSTRUCTION AND USE OF FARM IMPLEMENTS AND MACHINES. 

SECTION I. 

Plows and Plowing 130 

Trench and Subsoil Plowing 134 

The double Mould-board Trench Plow 135 

The Subsoil Plow 136 

Fowler's Draining Plow 136 

The Paring Plow— The Gang Plow 140 

A2 



X CONTENTS. 

SECTION II. 

Page 

Pulverizers 141 

The Harrow 141 

Cultivators 143 

Clod-crushers 146 

SECTION III. 

Sowing-machines 148 

Horse Rakes 152 

Mowing and Reaping Machines 156 

SECTION IV. 

Knee-joint Power 159 

Endless-chain Powers 164 

SECTION V. 

Application of Labor 167 

SECTION VI. 
Models of Machines 173 



PART II. 

HYDRODYNAMICS. 



CHAPTER I. 

HYDROSTATICS. 

SECTION I. 

Upward Pressure 176 

Measurement of Pressure at different Heights 178 

Determining the Strength of Pipes 179 

Springs and Artesian Wells 179 

SECTION II. 

Determining Pressure on Surfaces 180 

Hydrostatic Bellows 183 

Hydrostatic Press 184 

SECTION III. 
Specific Gravities 187 

CHAPTER II. 

HYDRAULICS. 

SECTION I. 

Velocity of falling Water 189 

Discharge of Water through Orifices and Pipes 190 



CONTENTS. XI 



SECTION II. 



Velocity of Water in Ditches 192 

Leveling Instruments 194 

SECTION III. 

HYDRAULIC MACHINES. 

Archimedean Screw 196 

Archimedean Root-washer 197 

Pumps 198 

Water-ram 200 

Water-engines 202 

Flash-wheel 203 

SECTION IV. 

WAVES. 

Nature of Waves 204 

The Water not progressive 205 

Breadth and Velocity of Waves 206 

Preventing the Inroads of Waves 208 

SECTION V. 

Contents of Cisterns 210 

Rule for determining the Contents 211 

Determining their Size ...... 212 



PART III. 

PNEUMATICS. 

CHAPTER I. 



PRESSURE OF AIR. 

Height and Weight of the Atmosphere 213 

The Barometer 216 

The Syphon 218 

CHAPTER II. 

MOTION OF AIR. 

SECTION I. 

Winds— Force of Wind 221 

Wind-mills for Farms 223 

Causes of Wind 227 



XU CONTENTS. 

SECTION II. 

Page 

Chimney Currents 227 

Construction of Chimneys 228 

Chimney-caps 229 

Ventilation 232 



PART IV. 
HEAT, 

CHAPTER I. 

CONDUCTION OF HEAT. 



SECTION I. 

Conducting Power of Bodies 235 

Utility of this Principle 236 

Conducting Power of Liquids 237 

SECTION II. 

Expansion by Heat 238 

The Steam-engine 241 

Exception to Expansion by Heat 246 

SECTION III. 

Latent Heat 248 

Advantages of Latent Heat — Latent Heat of Steam 249 

Green and dry Wood for Fuel 250 

CHAPTER II. 

Radiation of Heat 253 

Dew and Frost 255 

Frost in Valleys — Remarkable Effects of Heat on Water 256 



APPENDIX. 

Apparatus for Experiments 259 

Tables of Specific Gravities . : 263 

Weight of a cubic Foot of various Substances 264 

Discharge of Water through Pipes 264 

Velocity of Water in Pipes 265 

Rule for the Discharge of Water 266 



FARM IMPLEMENTS, 

AND THE 

PRINCIPLES OF THEIR CONSTRUCTION 
AND USE. 



PART I. 

MECHANICS. 



CHAPTER I. 

INTRODUCTION. 

No farm, even of moderate size, can be well fur- 
nished without a large number of machines and im- 
plements. Scarcely any labor is performed without 
their assistance, from the simple operations of hoeing 
and spading, to the more complex work of turning the 
sod and driving the thrashing-machine. It becomes, 
therefore, a matter of vital importance to the farmer 
to be able to construct the best, or to select the best 
already constructed, and to apply the forces required 
for the use of such machines to the best possible ad- 
vantage. 

A great loss occurs frequently from the want of a 
correct knowledge of mechanical principles. The 
strength of laborers is often badly applied by the use 
of unsuitable tools, and that of teams is partly lost by 
being ill adjusted for the best line of draught ; as, for 



14 MECHANICS. 

example, by a bad attachment to the plow for forcing 
its wedge-like form most effectively through the soil. 
We may perhaps see but few instances of so great a 
blunder as the man committed who fastened his 
smaller horse to the shorter end of the whipple-tree, 
to balance the large horse at the longer end ; or of the 
other man, who, when riding on horseback to mill, 
atop of his bag of grain, concluded to relieve the ani- 
mal by dismounting, shouldering the bag himself, and 
then remounting ; yet cases are not uncommon where 
other operations are performed to almost as great a 
disadvantage, and which, to a person well versed in 
the science of mechanics, would appear nearly as 
strange and absurd. 

The improvement of farm machines and tools with- 
in the last fifty years has probably enabled the farmer 
to effect twice as much work with the same force of 
horses and men. Plows turn up the soil deeper, more 
evenly and perfectly, and with greater ease of draught ; 
hoes and spades have become lighter and more efficient ; 
grain, instead of being beaten out by the slow and la- 
borious work of the flail, is now showered in torrents 
from the tluashing-macliine ; horse-rakes accomplish 
singly the work of many men using the old hand-rake ; 
twelve to twenty acres of ripe grain are neatly cut in 
one day with a two-horse reaper ; wheat drills, avoid- 
ing the tiresome drudgery of sowing by hand, are ma- 
terially increasing the amount of the wheat crop ; 
while a few farmers are making a large yearly saving 
by the application of horse-power to sawing wood, 
churning, driving washing-machines, and even to ditch- 
ing. A celebrated English farmer has lately accom- 



INTRODUCTION. 15 

plished even more ; for, by means of a steam-engine 
of six-horse power, he drives a pair of mill-stones for 
grinding feed, thrashes and cleans grain, elevates and 
bags it, pumps water for cattle, cuts straw, turns the 
grindstone, and drives liquid manure through pipes 
for irrigating his fields; and the waste steam cooks 
the food for his cattle and swine — all this work being 
performed hi a first-rate manner. 

Now these improvements were mainly effected 
through the knowledge of mechanical principles, and 
many of them would doubtless have been sooner 
achieved and better perfected if these principles had 
been well understood by farmers ; for, constantly using 
the machines themselves, they could have perceived 
just what defects existed, and, by understanding the 
reasons of those defects, have been able to suggest the 
remedies in a better manner than the mere manufac- 
turer. Moreover,, as the introduction of what is new 
and valuable depends greatly upon the call for them, 
farmers would have been prepared to decide with more 
confidence and certainty upon their real merits, and 
thus to increase and cheapen the supply of the best, 
and to reject the worthless. 

One great reason that farm implements are still so 
imperfect, is, that the farmers themselves do not fully 
understand what is needed, and how much may be yet 
accomplished. They have not enough knowledge of 
the principles of mechanics to qualify them for judging 
of the merits of new machines ; and, being afraid of 
imposition, often reject what is really valuable, or else, 
being pleased with a fine appearance, are easily de- 
ceived with empty pretensions. 



16 MECHANICS. 

The implements and machines which every farmer 
must have who does his work well are numerous and 
often costly. A farm of one hundred acres requires 
the aid of nearly all the following : two good plows, a 
small plow, a suhsoiler, a single and two-horse culti- 
vator, a drill-barrow, a roller, a harrow, a farming-mill, 
a straw-cutter, a root-sheer, a farm wagon with hay- 
rack, an ox-cart, a horse-cart, wheel-harrow, sled, shov- 
els, spades, hoes, hay-forks and manure-forks, hand- 
rakes and revolving rakes, scythes and grain-cradles, 
grain-shovel, maul and wedges, pick, axes, wood-saw, 
turnip-hook, hay-knife, apple-ladders, and many other 
smaller conveniences. The capital for thus furnishing 
in the best manner all the farms in the Union has 
been computed to amount to five hundred millions of 
dollars, and as much more is estimated to be yearly 
paid for the labor of men and horses throughout the 
country at large. 

To increase the effective force of labor only one fifth 
would, therefore, add annually one hundred millions in 
the aggregate to the profits of farming ; while on the 
other hand, if we look back fifty years to the imperfect 
implements then in use, we may at once perceive the 
vast amount saved by the improvements since made ; 
and when, especially, we notice the condition of bar- 
barous nations, and contrast that condition with our 
own — the former thinly scattered in comfortless hovels 
through far-stretching and gloomy forests, subsisting 
mainly by hunting and fishing, and often suffering 
from hunger and cold ; the latter blessed with smooth, 
cultivated fields, green meadows, and golden harvests, 
interspersed with comfortable farm-houses ; with the 



INTRODUCTION. 17 

hum of business through populous cities, and along 
far-reaching lines of canals and rail-roads, and ships 
for foreign commerce, freighted with the productions 
of the soil, threading every channel and whitening 
every sea— when we observe this contrast, we can 
not fail to be struck with the convincing proof that 
" knowledge is power," and of the loss sustained on 
the one hand from its absence, and the advantages on 
the other of availing ourselves of its accumulated 
stores. 



18 MECHANICS. 



CHAPTER II. 

GENERAL PRINCIPLES OF MECHANICS. 

SECTION I. 
GENERAL PROPERTIES OF MATTER. 

Having briefly pointed out some of the advantages 
to the farmer of understanding the principles of the 
machines he constantly uses, we now proceed to an 
examination of these principles. It will he most con- 
venient to begin with the simpler truths of the science, 
proceeding, as we advance, to their application in the 
construction of machines. 

The term matter is applied to whatever composes 
those substances which we perceive with our external 
senses ; and when we speak of a " body," we mean 
any thing composed of matter. Thus, wood, stone, 
water, and metal are matter ; while the mind and its 
qualities are not matter. A stone, a block of wood, a 
bag of sand, and any other mass of matter, are termed 
bodies. 

DIVISIBILITY. 

Matter possesses several general properties, the ex- 
amination of which is both useful and interesting. One 
of these is its divisibility, or capability of being divided 
into small parts, and again divided, so far as we know, 
without any limit. Many experiments show the great 
minuteness to which this division may be carried. For 



DIVISIBILITY. 19 

example, a gold leaf may be hammered till ^m of an 
inch in thickness, or one thousand times thinner than 
a leaf of this book. A silver wire may be coated with 
gold, and then drawn out so fine that the gold coating 
shall become a thousand times less than the gold leaf 
itself. So attenuated is one of the threads of a small 
spider's web, that half a pound would reach round the 
globe. It has been found that tripoli, a mineral used 
in the arts, is made up of shells of exceedingly minute 
animals, so small that a single cubic inch contains forty 
thousand millions, or fifty times as many individuals 
as there are human beings on the face of the earth. 
Hundreds of animalcules (or minute animals) have 
been seen with a microscope in a single drop of water, 
without in the least degree affecting its transparency. 
Some of these are so small that thousands could rest, 
without crowding, on the point of a pin; yet these 
have blood-vessels, muscles, and other parts, as well as 
larger animals. Still more minute appears to be the di- 
vision of those substances which are constantly throw- 
ing off odors or perfumes. A grain of musk will scent 
the air of a room for years, with particles inconceivably 
minute ; and a bed of flowers will fill the air with their 
odor, as hundreds of miles of the breeze successively 
pass over them, with an insensibly small portion of 
their own weight. 

But no division, however minute, ever destroys mat- 
ter ; every particle still retains its identity ; and the 
largest mountains, weighing millions of tons, are made 
up of these innumerable particles. 



20 MECHANICS. 

I MPE NETR ABILITY. 

Another property of matter is impenetrability, or 
the inability of two portions to occupy the same space 
at the same time. A nail driven into wood only 
crowds the particles of wood asunder. Sugar will 
dissolve in water, but the particles of the sugar oidy 
pass in between those of the water. Wood becomes 
soaked with water by its entering the pores of the 
wood. These pores are seen by means of a powerful 
microscope, and are so small that one million have 
been computed to exist in a space not larger than a 
five-cent piece. 

INDESTRUCTIBILITY. 

Another property is indestructibility. Matter is 
separated and changed in form from one body to an- 
other, but never destroyed. "When wood is burned in 
the fire, it disappears ; but it is found that the smoke, 
vapor, and ashes weigh as much as before, although in 
a different form. The flashing of gunpowder appears 
to destroy it wholly ; but if all the vapors and gases 
are retained within a vessel, they are found to weigh 
as much as the original solid. Growing plants derive 
all their weight from the soil and air; they decay 
again, and form the manure for new plants ; but none 
of their particles are lost. They furnish food for ani- 
mals, or are manufactured into different substances, 
and, in all the changes they undergo, still retain their 
existence. 



INERTIA. 21 

INERTIA. 

There is still another and very important quality of 
all material bodies, called inertia. This term express- 
es their passive state — that is, that no hody (not hav- 
ing life), when at rest, can move itself, nor, when in 
motion, can stop itself. A stone can not commence 
rolling of its own accord ; a carriage can not travel on 
the road without being drawn ; a train of cars can not 
commence gliding upon the rails without the power of 
the locomotive. 

On the contrary, a body, when once set in motion, 
will continue in motion perpetually, unless stopped by 
something else. A cannon ball rolled upon the ground 
continues rolling till its force is gradually overcome 
by the resistance of the rough earth. If a polished 
metallic globe were driven swiftly on a level and pol- 
ished metallic plane, it would continue in motion a 
long time and travel to a great distance ; but still the 
extremely minute roughness of the surfaces, with the 
resistance of the air, would continually diminish its 
speed until finally stopped. A wheel made to spin on 
its axis continues till the friction at the axis and the 
impeding force of the air bring it to rest. But if the 
air is first removed by means of an air-pump, the mo- 
tion will continue much longer. Under a glass re- 
ceiver, thus exhausted, a top has been made to spin 
for hours, and a pendulum to vibrate for a day. The 
resistance of the air may be easily perceived by first 
striking the edge and then the broad side of a large 
piece of pasteboard against the air of a room. It is 
further shown by means of an interesting experiment 



22 



MECHANICS. 




with the air-pump. Two fan-wheels, made of sheet 

Fig. 1. tin, one (a) striking the air with 

its edges, and the other (b) with 

its broad faces (Fig". 1), are set in 

motion alike ; b is soon brought to 

rest, while a continues revolving a 

long time. If now they are placed 

under the receiver of an air-pump, 

the ah* exhausted, and motion given 

to them alike by the rack-work d, 

Fans revolving in a vacuum, they will both continue in motion 

during the same period. 

There is no machinery made by man free from the 
checking influence of friction and the air ; and for this 
reason, no artificial means have ever devised a perpet- 
ual motion by mechanical force. But we are not with- 
out a proof that motion will continue without ceasmg 
when nothing operates against it. The revolutions of 
the planets in their orbits* furnish a sublime instance ; 
where removed from all obstructions, these vast globes 
wheel round in their immense orbits, through success- 
ive centuries, and with unerring regularity, preserving 
undiminished the mighty force given them when first 
launched into the regions of space. 

To set any body in motion, a force is requisite, and 
the heavier the body, the greater must be the force. A 
small stone is more easily thrown by the hand than a 
cannon ball ; speed is much more easily given to a skiff 
than to a large and heavy vessel ; but the same force 
which sets a body in motion is required to stop it. 
Thus, a wheel or a grindstone, made to revolve rapidly, 
would require as great an effort of the arm to stop it 



INERTIA. 



23 




Inertia Apparatus. 



suddenly as to give it sudden motion. An unusual 
exertion of the team is required in starting a loaded 
wagon ; "but when once on its way,, it would require 
the same effort of the horses to stop it as to back it 
when at rest. 

The force of inertia is finely exhibited by means of a 
little instrument called the iner- 
tia apparatus (Fig. 2). A mar- 
ble or small ball is placed on a 
card (c) resting on a concave 
stand. A spring snap is then 
made to strike the card, throwing 
it to a distance, but leaving the 
ball upon the hollow end of the stand. The same ex- 
periment may be easily performed by placing a very 
small a~*?le or other solid on a card, the whole resting 
on a common sand-box, or even the hollow of the hand. 
A sudden snap with the finger will throw the card 
away, while the apple will drop into the cavity. The 
following experiment is still more striking: Procure 
a thread just strong enough to bear three 
pounds, and hang upon it a weight of 
two pounds and a half. Another half 
pound would break it. Now tie an- 
other thread, strong enough to bear one 
pound, to the lower hook of the weight. 
If the lower thread be pulled grad- 
ually, the upper thread will of course 
break ; but if it be pulled with a jerk, 
the lower thread will break. If the 
jerk be very sudden, the lower string 
will break, even if it be considerably 



Fig. 3. 




24 MECHANICS. 

stronger than the upper, the inertia of the weight re- 
quiring a great force to overcome it suddenly. The 
threads used in this experiment may be easily had of 
any desired strength by taking the finest sewing cot- 
ton, and doubling to any required extent. 

This experiment shows the reason why a horse, when 
he suddenly starts with a loaded wagon, is in danger 
of breaking the harness ; and why a heavier weight 
may be lifted with a windlass or pulley having a weak 
rope, if the strain is gradual and not sudden. For the 
same reason, glass vessels full of water are sometimes 
broken when hastily lifted by the handle. "When a 
bullet is fired through a pane of glass, the inertia re- 
tains the surrounding glass in its place during the mo- 
ment the ball is passing, and a round hole only is 
made ; while a body moving more slowly, and pressing 
the glass for a longer space of time, fractures the whole 
pane. 



section n. 

MOMENTUM. 



The force which a moving body has to continue on- 
ward is called its momentum ; it is, in fact, the inertia 
of a moving body. When a force is first applied to 
any heavy body, it moves slowly ; but the little mo- 
mentum it thus acquires, added to the continued force, 
increases the velocity. This increase of velocity is 
of course attended with increased momentum, which 
again, added to the acting force, still further quickens 
the speed. For this reason, when a steam-boat leaves 
the pier, and its paddle-wheels commence tearing 



MOMENTUM. 25 

through the water, the motion, at first slow, is con- 
stantly accelerated till the increasing resistance of the 
water to the moving mass becomes equal to the strength 
of the engine and the momentum.* Were it not for 
the momentum of moving bodies (inertia existing), 
no speed ever could be given to any heavy body, as a 
carriage, boat, or train of cars. 

The chief danger in fast riding, or fast traveling of 
any kind, is from the momentum given to the trav- 
eler. If a rail-way passenger should step from a car 
when in full motion, he would strike the earth with 
the same velocity as that of the train ; or if the train 
at thirty miles an hour should be instantly stopped, 
the passengers would be pitched forward with a swift- 
ness equal to thirty miles an hour. When a horse 
suddenly stops, the momentum of the rider tends to 
throw him over the horse's head. When a wagon 
strikes an obstruction, the driver falls forward. A 
case in court was once decided against the plaintiff, 
who claimed that the defendant had driven against his 
wagon with such force as to throw the plaintiff to a 
great distance ; but the fact was shown that by such 
momentum he himself must have been driving furi- 
ously, and not the defendant, and he lost his suit. 

An African traveler once succeeded in saving his 
life by a ready knowledge of this principle. He was 
closely pursued by a tiger, and when near a precipice, 
watching his opportunity, he threw his coat and hat 

* In ordinary practice, this is not strictly correct, as friction will 
make some difference. This influence will he more particularly 
considered on a subsequent page. Its omission here does not at all 
alter the principle under consideration. 

B 



26 



MECHANICS. 



Fig. 4. 



V 



on a bush, and jumped one side, when the animal, 
leaping swiftly on the concealed bush, was carried by 
momentum over the precipice. 

As a large or heavy body possesses greater moment- 
um than a small or light one, so any body moving with 
great speed possesses more than one moving slowly; 
for instance, the momentum of a 
rifle ball is so great as to carry it 
through a thick plank, while, if 
thrown slowly, it would scarcely 
indent it. 

This property of bodies is ap- 
plied with great advantage to 
many practical purposes. The 
momentum of the hammer drives 
the nail into the wood; for the 
mere pressure of its weight would 
not do it, if it were a hundred 
times as heavy. Wedges are 
driven by employing the same 
kind of power. 

On a larger scale, the pile-en- 
gine operates in a similar man- 
ner. The ram or weight, h (Fig-. 
4), is slowly lifted by means of a 
pulley and wheel- work, worked 
|o» by the handles or cranks, b b, un- 
ll-i^ til the arms of the tongs which 
■" hold the ram are compressed in 
the cheeks, i i, when it sudden- 
ly falls with prodigious force on 
In this way long posts of 




Pile Engine. 

the pile or post to be driven. 



THE FLY-WHEEL. 



27 



great size are forced into the mud of swamps and riv- 
er bottoms, where other means would fail. When a 
steam-engine is used for lifting the ram, the work is 
more rapidly performed. 

An interesting example of the use and efficiency of 
momentum is furnished by the water-ram, a machine 
for raising water, described on a subsequent page. 



THE FLY-WHEEL. 



The, fly-wheel, a large and heavy wheel used to reg- 
ulate the motion of machinery, derives its value from 
the power of inertia, or momentum, which prevents the 
machine from stopping suddenly when it meets with 
any unusual obstruction. In the common thrashing- 
machine, it has been found that a heavy cylinder, by 
acting as a fly-wheel, renders the motion steadier, and 
less liable to become impeded by large sheaves of grain. 
An ignorance of this principle has sometimes proved a 
serious inconvenience. A farmer, having occasion to 
raise a large quantity of water, erected a horse-pump ; 
but at every stroke of the pump the animal was sud- 
denly thrown loosely forward, and again jerked back- 
ward, as the piston fell lightly and rose heavily. A 
fly-wheel attached to the machinery would have pre- 
vented this unpleasant jerking, and have enabled the 
horse, in consequence, to accomplish more work. In 
the pile-driving engine, where a great weight is sud- 
denly thrown loose from a height, the horses would be 
pitched forward when suddenly relieved of this load, 
but for the regulation of a fly-wheel, the motion of 
which is not quickly changed, neither from fast to slow 
nor from slow to fast. 



28 



MECHANICS. 



Fig. 5. 




Where there is a rapid succession of forces required 

in practice, the fly-wheel 
is usually of great advan- 
tage. Hence its use in all 
revolving straw-cutters, 
where the knives make 
quickly-repeated strokes 
(Fig. 5). More recently 
it has been applied to the 

Straw-cutter with fly-wheel. dasher - chum (Fig. 6), 

where the rapid upright strokes 
are so well known to be very fa- 
tiguing for the amount of force 
applied. 

By thus regulating motion, 
the fly-wheel frequently enables 
an irregular force to accomplish 
work which otherwise it could 
not perform. Thus a man may 
exert a force equal to raising a 
hundred pounds, yet, when he 
turns a crank, there is one part 
of the revolution where he 
works to great disadvantage, and where his utmost 
force will not balance forty pounds. Hence, if the 
work is heavy, he may not be able to turn the crank, 
nor to do any work at all. If, however, a fly-wheel be 
applied, by gathering force at the most favorable part 
of the turning, it carries the crank through the other 
part. 

An error is sometimes committed by supposing the 
fly-wheel actually creates power, for as much force is 




Churn with a fly-wheel. for equal- 
izing the motion. 



THE PLY-WHEEL. 29 

required to give it momentum as it afterward imparts 
to the machine ; it consequently only accumulates and 
regulates power. 

A curious example of the effect of momentum is 
shown in the failure and success of two different modes 
of constructing wire fences with very slender wires for 
the boundaries of pastures. The unsuccessful mode 
consisted of tightly-stretched wires between solid posts 
not more than twelve to twenty feet apart. A side 
strain of only a few inches was enough to snap the 
wires; consequently, a bullock plunging blindly against 
them could not be quickly enough checked in his mo- 
mentum, and such fences were therefore nearly useless 
without stronger wire. The successful mode was to 
stretch the wires well between strong and deeply-set 
posts some hundreds of feet apart, the intervening space 
being kept even by upright bars, but not posts. "When 
an animal accidentally struck this fence, the great 
length permitted it to yield sidewise far enough to ex- 
pend the momentum without rupture, when its elas- 
ticity at once threw it back to its former place. 

On rough roads, the force of inertia causes a severe 
strain to a loaded wagon when it strikes a stone. The 
horses are chafed, the wagon and harness endangered, 
and the load jarred from its place. This inconvenience 
is avoided in part by placing the box upon springs, 
which, by yielding to the blow, gradually lessen the 
effects of the shock. For carts and slowly - moving 
lumber- wagons their advantages are considerable, but 
much greater as the velocity and momentum increase. 
Even on so smooth a surface as a rail-road, it was 
found, by experiments made some years ago, that when 



30 MECHANICS. 

the machinery of a locomotive was placed upon springs, 
it would endure the wear and tear of use four times as 
long as without them. 

For this reason, a ton of stone, brick, or of sand is 
more severe for a team than a ton of wool or hay, which 
possesses considerable elasticity. 

ESTIMATING THE QUANTITY OF MOMENTUM. 

The quantity of momentum is estimated by the ve- 
locity and weight of the body taken together. Thus 
a ball of two pounds' weight moves with twice the force 
of a one-pound ball, the speed being equal ; a ten-pound 
ball with ten times the force, and so on. A body mov- 
ing at the rate of two feet per second possesses twice 
the momentum of another of equal size with a velocity 
of only one foot per second. A musket ball, weighing 
one ounce, flying with fifty times the speed of a cannon 
ball, weighing fifty ounces, would strike any object 
with equal force ; or, if they should meet each other 
from opposite directions, the momentum of both would 
be mutually destroyed, and they would drop to the 
earth. 

Where the mass is very great, even if the motion is 
slow, the momentum is enormous. A large ship float- 
ing near a pier wall may approach it with so small a 
velocity as to be scarcely perceptible, and yet the force 
would be enough to crush a small boat. When great 
weight and speed are combined, as in a rail- way loco- 
motive, the force is almost irresistible. This circum- 
stance often insures the safety of the passengers ; for 
as nothing is capable of instantly overcoming so pow- 
erful a momentum, when accidents occur the speed is 



COMPOUND MOTION. 31 

more gradually slackened, and the passengers are not 
pitched suddenly forward. A light wagon, rapidly 
driven, possessing but little comparative force, is more 
suddenly arrested, and the danger is greater. 

"When two bodies meet from opposite directions, each 
sustains a shock equal to the united forces of both. 
Two men accidentally striking, even if walking mod- 
erately, receive each a severe blow ; that is, if each 
were walking three miles an hour, the shock would be 
the same as if one at rest were struck by the other 
with a velocity of six miles an hour. This principle 
accounts for the destructive effects of two ships run- 
ning foul of each other at sea, or of the collision of two 
opposite trains on a rail-road. 

The preceding principles show that a sledge, maul, 
or ax will always strike more effective blows when 
made heavier, if not rendered unwieldy. 



SECTION" III. 

COMPOUND MOTION. 



It often happens that two or more forces act on the 
same body at the same time. If they all act in the 
same direction, the effect will be equal to the sum of 
the forces taken together ; but if they act in opposite 
directions, the forces will tend to destroy each other. 
If two equal forces act in contrary directions, they will 
6e completely neutralized, and no motion will be pro- 
duced. Thus, as an example of these forces — a bird 
flying at the rate of forty miles an hour, with a wind 
blowing forty miles an hour, will be driven onward by 
these two combined forces eighty miles an hour ; but 



isa 



MECHANICS. 




if it undertake to fly against such a wind, it will not 
advance at all, but remain stationary. A similar re- 
sult will take place if a steam-boat, having a speed of 
ten miles an hour, should first run down a river with a 
current of equal velocity, and then upward against the 
current ; in the first case it would move twenty miles 
an hour, and in the latter it would not move at all. 
Where forces act neither in the same nor in opposite 
Fig. 7. directions, hut obliquely, the re- 

sult is found in the following 
manner : If a ball, placed at the 
point a (Fig. 7), be struck by 
two different forces at the same 
moment, in the direction shown 
by the two arrows, and if one 
force be just sufficient to carry it from a to c, and the 
other to carry it from a to b, then it will move inter- 
mediate between the two, in the direction of the diag- 
onal of the parallelogram a d, and to a distance just 
equal to the length of this diagonal or cross-diameter. 
When the forces act very nearly together, the paral- 
lelogram of the forces will be very narrow and quite 

long, with a long di- 
agonal (Fig. 8) ; but 
if they act on nearly 
opposite sides of the 
ball, they will very nearly neutralize each other, and the 
Fig. 9. diagonal or result will be 

very short, showing that 
the motion given to the ball 
will be very small ( Fig. 9. ) 
These examples show the importance of having 




COMPOUND MOTION. 



33 



teams attached to a plow or to a wagon very nearly 
in a straight line with the draught, or else a part of 
the force will he lost ; and also the importance, when 
several animals are drawing together, of their working 
as nearly as possible in the same straight line. For, 
the more such forces deviate from a right line, the 
more they will tend to destroy or neutralize each other. 

A familiar example of the result of two oblique forces 
is furnished when a boat is rowed across a river. If 
the river has no current, the boat will pass directly 
from bank to bank perpendicularly ; but if there is a 
current, its track will form a diagonal, and it will 
strike the opposite bank lower down, according to the 
rapidity of the stream and the slowness of the boat. 

Another instance is afforded when a ferry-boat is 
anchored, by means of a long rope, to a point some 
distance above (Fig. 10); the boat being turned 

Fig. 10. 




obliquely, will pass from' one bank to the other by the 
force of the current. Here the water tends to carry 
the boat downward, while the force of the rope acts 
upward ; the boat passes between the two from bank 
to bank. The ascent of a kite is precisely similar, the 
wind and the string being counteracting forces. "When 
a vessel sails under a side-wind, the resistance of the 
keel against the water, and the force of the wind 
against the sail, act in different directions, and pro- 
duce a motion of the vessel between them. 

B2 



34 MECHANICS. 

CENTRIFUGAL FORCE. 

All bodies, when in motion, have a tendency to move 
forward in a straight line. A stone thrown into the air 
is gradually bent from this straight course into a curve 
by the attraction of the earth. When a ball is shot 
from a gun, the force being greater, it flies in a longer 
and straighter curve. A familiar example also occurs, 
while driving a wagon rapidly, in attempting to turn 
suddenly to the right or left ; the tendency of the load, 
to move straight on will sometimes cause its overthrow. 
An observance of this principle would prevent the error 
which some commit by making sharp turns or angles in 
ditches and water-courses ; the onward tendency of the 
water drives it against the bank, checks its course, and 
wears away the earth. By giving the ditch a curve, 
the water is but slightly impeded, and a much larger 
quantity will escape through a channel of any given size. 

When a grindstone is turned rapidly, the water upon 
its surface is thrown off by this tendency to move in 
straight lines. In the same way, a weight fastened to 
a cord, whirled by the hand, will keep the cord stretch- 
ed during the revolution. The same principle causes 
a stone, when it leaves a sling, to fly off in a line. This 
tendency to fly off from a revolving centre is called 
centrifugal force — the word centrifugal meaning fly- 
ing from the centre. Large grindstones, driven with 
great velocity by machinery, are sometimes split asun- 
der by centrifugal force. 

The most sublime examples of centrifugal force oc- 
cur in the motion of the earth and planets, which will 
be more fully explained on a future page. 



GRAVITATION. 35 



CHAPTER III. 

ATTRACTION. 

SECTION - I. 

GRAVITATION. 

The earth, as is well known, is a mass of matter in 
the form of a globe, the diameter being upward of 
7900 miles. From its enormous size and the small 
portion seen from one point, the surface appears flat, 
except where broken into mountains and valleys. 

The tendency which all bodies possess of falling to- 
ward the earth is owing to the attractive force which 
this great mass of matter exerts upon them. This kind 
of attraction is called gravitation. The force with 
which a body is thus drawn is the weight of that body. 

When a stone is dropped from the hand, its velocity 
is at first slow, but continues to increase till it strikes 
the earth ; hence, the further it falls, the harder it will 
strike. This accelerated motion is precisely similar to 
that of a steam-boat when it first leaves the wharf; the 
force of gravity may be compared to the driving power 
of the engine, and the quickened velocity of the falling 
stone to the increased headway of the boat. 

All bodies, whether large or small, fall equally fast, 
unless they are so light as to be borne up in part by 
the resistance of the air. In the first second of time 
they fall 16 feet ; in the next second, 3 times 16, or 
48 feet ; in the third second, 5 times 16, or 80 feet, and 
so on. Or, if the whole distance fallen be taken togeth- 



36 



MECHANICS. 



er, they fall 16 feet in one second, 4 times 16 in two 
seconds, 9 times 16 in three seconds, and so forth. In 
other words, the whole distance is equal to the square 
of the time. This is plainly exhibited by the following 
table :* 



Seconds, from beginning 
to fall. 


1 


2 


3 


4 


5 


6 


Whole height fallen in 
feet. 


16 


4X16 
or 64. 


9X16 
or 144. 


16X16 
or 256. 


25X16 
or 400. 


36X16 
or 576. 


Space fallen in each sec- 
ond in feet. 


16 


3X16 
or 48. 


5X16 
or 80. 


7X16 
or 112. 


9X16 
or 144. 


11X16 
or 176. 



A stone or other body will fall 1 foot in a fourth of 
a second, 3 feet the next fourth, 5 feet the third fourth, 
and 7 feet the last fourth ; which is the same as 4 feet 
in half a second, 9 feet in three fourths of a second, and 
16 feet for the whole second. 

The depth of an empty well, or the height of a prec- 
ipice, may be nearly ascertained by observing the 
time required for the fall of a stone to the bottom. 
The time may be measured by a stop-watch, or, in its 
absence, a pendulum may be made by fastening a peb- 
ble to a cord, which will swing from the hand in reg- 
ular vibrations of an exact second each if the cord be 
39£ inches long, or of half a second each if it be about 
9 1 inches long. 

The velocity increases simply as the time — that is, 
the speed in falling is twice as great in two seconds 
as in one ; three times as great in three seconds ; four 
times as great in four seconds, and so forth. A stone 
will fall four times as far in two as in one second, while 

* The distance, accurately stated, is sixteen feet and one inch for 
the first second, and hence the numbers in the table fall a very little 
short of the distance actually fallen. 



GRAVITATION. 37 

its velocity will be doubled ; nine times as far in three 
seconds, while its velocity will be tripled, &c. 

If a stone is thrown upward, its motion continues 
gradually to decrease, at the same rate as it increases 
in falling; hence the same time is required to reach 
its highest point, as to fall from that point back to the 
earth. Therefore the velocity with which it is first 
projected upward is equal to the velocity which it at- 
tains at the moment of striking the ground. There is 
an exception, however, to this general rule. In a vac- 
uum it would be perfectly correct, but in ordinary prac- 
tice the resistance of the air tends to diminish the ve- 
locity while as cending, and still further to retard it while 
descending. For this reason, it will fall with less speed 
than it first arose. For heavy bodies and small dis- 
tances, this exception would be imperceptible; but 
with small bodies falling from great heights, the differ- 
ence will be considerable. 

The velocity of a stone after falling one second, or 
sixteen feet, is at the rate of thirty-two feet per second ; 
hence, if thrown upward at that rate, it will rise just 
sixteen feet high. After falling three seconds, the rate 
is ninety-six feet; and hence, if projected upward at 
ninety-six feet per second, it will rise nine times sixteen 
feet, or one hundred and forty-four feet high. And so 
of other heights. 

Were it not for the resistance of the air, a feather 
would fall as swiftly as a leaden ball. This is conclu- 
sively shown by an interesting experiment. A tall glass 
jar (Fig-. 11), open at the bottom, is covered with a 
brass cap, fitting it air-tight. Through this cap passes 
an air-tight wire, which, by turning, opens a small pair 



38 



MECHANICS. 



Fig. 11. 

I 

TT 




of pincers. "Within these are placed 
a feather and a half dollar, and the 
air is then thoroughly drawn from the 
receiver hy means of an air-pump. 
The wire is turned, and the feather 
and coin hoth drop at once, and strike 
the bottom at the same moment. 



MEASURING THE VELOCITY.' 
wood's MACHINE. 



-AT- 




Feather ajid coin^ 
alike in a vacuwn 



In consequence of the swiftness of 
falling bodies, it is not easy to meas- 
ure the exact distance through which 
they fall in a given time. There is an 
instrument, however, known as At- 
ivood's Machine, which renders their 
motion much slower, at the same time 
./ailing ma t the rate of increase in velocity is 
precisely the same, and it Fi g . 12. 
therefore admits of an exact measurement of &l 
the descent. The principle of this machine /lJLj 
may be easily understood by Fig. 12, where \JL^ 
two weights, hung on a fine silk cord run- 
ning over a wheel, exactly balance each oth- 
er. If now a small additional weight be 
placed on one of these, it will destroy the bal- 
ance, and the weight will begin to move 
downward. As this little weight has to impart mo- 
mentum to both the other larger weights, they will 
move as much slower than ordinary falling as the 
smaller weight is less than they. On this principle 
Atwood's Machine, represented by Fig. 13, is made. 



MEASURING THE VELOCITY. 



39 



Fig. 13. 



The two weights are first made to 
halance each other, when one of 
them is raised nearly to the wheel 
at c, and a small weight in the form 
of a short rod is placed across it. 
It immediately descends with ac- 
celerated or increasing velocity un- 
til it reaches the hole in the shelf a, 
through which the weight passes, 
but the rod is caught and retained. 
The motion is now no longer accel- 
erated, because the weights have 
become equal, and the descending 
one Continues to fall uniformly at 
the same rate that it passed through 
the hole in the shelf, until it strikes 
the bottom. During this time its 
velocity may be accurately meas- 
ured by means of the clock and pen- 
dulum attached to the instrument. 
By sliding the shelf up or down, the 
velocity, after falling through different spaces to reach 
the shelf, may be accurately determined. When the 
shelf is placed very near the top, so that but little ve- 
locity is acquired, the descending weight will move 
very slowly all the way down ; but when placed low- 
er, the weight continues downward more rapidly. It 
is necessary that the wheel turn with extreme ease, to 
effect which, friction-wheels, described hereafter, are 
usually employed. 

There are many instances showing the accelerated 
motion and increased force of falling bodies. "When a 




Atwood's Machine for 
measuring the de- 
scent of bodies. 



40 MECHANICS. 

large stone rolls down a mountain, it first moves slow- 
ly, but afterward bounds with rapidity, sweeping be- 
fore it all smaller obstacles. Hail-stones, although 
small, acquire such velocity as to break windows ; and 
but for the resistance of the air, they would be much 
more destructive. The blow of a sledge-hammer is 
more severe as it is lifted to a greater height. New- 
ton was first led to the examination of the laws of 
gravity by observing, when sitting under an apple-tree, 
that the fruit struck his hand with greatest severity 
when it fell from the top of the tree. 

It is not an unusual error to suppose that a large 
body will fall more rapidly than a small one. Some 
can scarcely believe that a fifty-six pound weight will 
not drop with a greater velocity than a small nail, not 
remembering that a proportionately greater force is re- 
quired to overcome the inertia and set the larger body 
in motion. This error existed for many centuries, from 
the time of Aristotle until Galileo first questioned its 
correctness. The celebrated experiment which estab- 
lished the truth on this subject, and led to the discov- 
ery of the laws of falling bodies just explained, and 
which formed an era in modern philosophy, was per- 
formed from the top of the leaning tower of Pisa. 
Galileo was a philosophical teacher, and, being a man 
who thought for himself, soon discovered, by reasoning, 
the errors that had been received without a doubt for 
more than twenty centuries. All the learning of the 
age and the wisdom of the universities were against 
him, and in favor of this time-honored error, the truth 
of which no one had ever thought of submitting to ex- 
periment. The hour of trial arrived, when he, an ob- 



MEASURING THE VELOCITY. 41 

scure young man, stood nearly alone on one side, while 
the multitude, with all the power and confessed knowl- 
edge of the age, were on the other. 

The balls to be employed were carefully weighed 
and scrutinized to detect deception, and the parties 
were satisfied. The one ball was exactly twice the 
weight of the other. The followers of Aristotle main- 
tained that when the balls were dropped from the top 
of the tower, the heavy one would reach the ground in 
exactly half the time employed by the lighter ball. 
Galileo asserted that the weights of the balls would 
not affect their velocities, and that the times of descent 
would be equal. The balls were conveyed to the sum- 
mit of the lofty tower — the crowd assembled round the 
base — the signal was given — the balls were dropped at 
the same instant, and swiftly descending, at the same 
moment struck the earth. Again and again the ex- 
periment was repeated with uniform results. Galileo's 
triumph was complete— not a shadow of doubt remain- 
ed ; but, instead of receiving the congratulations of 
honest conviction, private interest, the loss of place, 
and the mortification of confessing false teaching, 
proved too strong for the candor of his adversaries. 
They clung to their former opinions with the tenacity 
of despair, and he was driven from Pisa.* 
* Mitchell's Lectures. 



42 MECHANICS. 



section n. 

COHESION. 

The attraction of gravitation, as we have just seen, 
takes place between bodies at a greater or less distance 
from each other. There is another kind of attraction, 
acting only when the parts of substances are in actual 
contact ; this is called cohesion. It is this which 
holds the parts of a body together and prevents it from 
falling to pieces. It may be shown by taking two 
pieces of lead, and, after having made upon them two 
smoothly-shaven surfaces with a knife, pressing them 
Fig. H. firmly together with a 

twisting motion (Fig. 14). 
The asperities of the sur- 

Cohesive attraction in two lead balls. faces are thus pushed 

down, and the particles are brought into close contact, 
so that cohesion immediately takes place between them, 
and some force will be required to draw them asunder.* 
Two pieces of melted wax adhere together in the same 
way. Melted pitch or other similar substance, smeared 
thinly over the polished surfaces of metal or glass, also 
causes cohesion to take place between them. Smooth 
iron plates, two inches in diameter, have been made to 
stick together so firmly with hot grease as to require, 
when cold, a weight of half a ton to draw them apart. 
Plates of brass of the same size, cemented by means 

* That this is not atmospheric pressure, like that -which holds two 
panes of wet glass together, is shown by the fact that it requires 
nearly as great a force to separate them "when they are placed under 
the exhausted receiver of an air-pump. Besides this, atmospheric 
pressure is much weaker than this force, with so small a surface. 




STRENGTH OP MATERIALS. 43 

of pitch, required 1400 pounds. On this principle de- 
pends the efficacy of those substances which are used 
for cementing broken vessels. 

The most perfect artificial polish which can be given 
to hard metals is still so rough as to prevent the faces 
from coming into close contact ; hence they must be 
either melted, or softened like iron when it is welded. 

The different degrees of cohesion which take place 
between the particles of various soils, to reunite them 
after they have been crumbled asunder, occasion the 
main difference between light and heavy soils. "When 
a light soil becomes soaked with water, the particles 
adhere in a very slight degree ; and hence, when it be- 
comes dry again, it is easily worked mellow. But if 
it be of a clayey nature, too much moisture softens it 
like melted wax : the particles are thus brought into 
close contact, and strong adhesion takes place ; hence 
the hardness and difficulty of working such soils when 
again dried. This adhesion is lessened by applying 
sand, chip-dirt, straw, yard-manure, or by burning the 
earth, but more especially by thorough draining, which, 
preventing the clay from becoming so moist and soft, 
lessens the adhesion of its' parts. 

Different substances are hard, soft, brittle, or elastic, 
according to the different degrees or modes of action 
in the attraction of cohesion. 

STRENGTH OF MATERIALS. 

It is a matter of great utility in the arts to determ- 
ine the different degrees of cohesion possessed by the 
different substances; or, in other words, to ascertain 
their strength. This is done by forming them into 



44 MECHANICS. 

rods of equal size, and applying weights to their lower 
extremities sufficient to break them, by drawing them 
asunder. The amount of weight shows their relative de- 
grees of strength. The following table gives the weights 
required to break the different substances, each being 
formed into a rod one quarter of an inch square : 

Woods. 

Ash, toughest 1000 lbs. 

Beech 718 " 

Box 1250 " 

Cedar 712 " 

Chestnut 656 " 

Elm 837 " 

Locust 1280 " 

Maple 656 " 

Oak, white 718 " 

Pine, white 550 " 

" pitch 750 " 

Poplar 437 " 

Walnut 487 " 

Metals. 

Steel, best 9370 lbs. 

" soft 7500 " 

Iron, wire 6440 " 

" best bar 4690 " 

" common bar 3750 " 

" inferior bar 1880 " 

" cast 1150 to 3100 " 

Copper, wire 3800 " 

cast 2030 " 

Brass 2800 " 

Platina wire '. 3300 " 

Silver, cast 2500 " 

Gold, cast 1250 " 

Tin 310 " 

Zinc, cast 160 " 

" sheet 1000 " 

Lead, cast 55 " 

" milled 207 " 



STRENGTH OF MATERIALS. 45 

From these tables we may ascertain the strength of 
chains, rods, &c, when made of different metals, and 
of timbers, bars, levers, swing-trees, and farm imple- 
ments, when made of woods. Wood which will bear 
a very heavy weight for a minute or two will break 
with two thirds of the weight when left upon it for a 
long time. This explains the reason that store-house 
and barn timbers sometimes give way under heavy 
loads of grain, which have appeared at first to stand 
with firmness. 

Although the preceding table gives the strength of 
wood drawn lengthwise, yet the comparative results 
are not greatly different when the force is applied in a 
transverse or side direction, so as to break in the usual 
way. 

The following table shows the results of several ex- 
periments with pieces of wood one foot in length, one 
inch square, with the weight suspended from one end, 
bending them sidewise. 

White oak, seasoned, broke with 240 lbs. 

Chestnut, " " 170 " 

White pine, " " 135 " 

Yellow pine, " "■ 150 " 

Ash, " " : 175 '■' 

Hickory, " " 270 " 

A rod of good iron is about ten times as strong as 
the best hemp rope of the same size. The best iron 
wire is nearly twenty times as strong as a hemp cord. 
Hence the enormous strength of the wire cables, sev- 
eral inches in diameter, which are employed for the 
support of suspension bridges. 

A rope one inch in diameter will bear about 5000 
lbs., but in practice should not be subjected to more 



46 MECHANICS. 

than half this strain, or about one ton. The strength 
increases or diminishes according to the size of the 
cross-section of the rope ; thus a cord half an inch in 
diameter will support one quarter as much as an inch, 
and a quarter-inch cord a sixteenth as much. A knowl- 
edge of the strength of ropes, as used hy farmers in 
windlasses, pulleys, drawing loads, &c, would some- 
times prevent serious accidents by their breaking. The 
following table may therefore be useful : 

Diameter of rope or Pounds borne Breaking 

cord in inches. with safety. weight. 

One eighth 31 lbs. *78 lbs. 

One fourth 125 " 314 " 

One half 500 " 1250 " 

One 2000 " 5000 " 

One and a quartei' 3000 " 7500 " 

One and a half 4500 " 12,500 " 

These results will vary about one fourth with the 
quality of common hemp. Manilla is about one half 
as strong as the best hemp. The latter stretches one 
fifth to one seventh before breaking. 

Wood is about seven to twenty times stronger when 
taken lengthwise with the fibres than when a side 
force is exerted, so as to split it. The splitting of tim- 
ber or wood for fuel is, however, accomplished with a 
comparatively small power by the use of wedges, the 
force of heavy blows, and the leverage of the two parts. 

The attraction of cohesion is very weak in liquids ; 
it is sufficient, however, to give a round or spherical 
shape to very small portions or single drops, and to fur- 
nish a beautiful illustration, on a minute scale, of the 
same principle which gives a rounded form to the sur- 
face of the sea. In one case, cohesion, by drawing to- 
ward a common centre, forms the minute globule of 



CAPILLARY ATTRACTION. 



47 



dew upon the blade of grass ; in the other, gravitation, 
acting in like manner, but at vast distances, gives the 
mighty rotundity to the rolling waters of the ocean. 



CAPILLARY ATTRACTION. 



Capillary attraction is a species of cohesion; it 
takes place only between solids and liquids. It is this 
which holds the moisture on the surface of a wet body, 
and which prevents the water from running instantly 
out of a wet cloth or sponge. By touching the lower 
extremity of a lump of sugar to the surface of water 
in a vessel, capillary attraction will cause the water to 
rise among its granules and moisten the whole lump. 
It may be very distinctly shown by placing the end of 
a fine glass tube into water ; the water will rise in it 
above the level of the surrounding surface. If the bore 
of the tube be the twelfth of an inch in diameter («, 
Fig. 15), it will rise a quarter of an inch; if but the 

Fig. 16. 




Capillary attraction in tubes. Capillary attraction between two panes of 

glass. 

twenty-fifth of an inch in bore, as b, it will rise half an 
inch ; but if only a fiftieth of an inch, the water will 
rise an inch. This ascent of the liquid is caused by 
the attraction of the inner surface of the tube, until the 



48 MECHANICS. 

weight of the column becomes equal to the force of the 
attraction. Capillary attraction may he also exhibited 
by two small plates of glass, placed with their edges in 
water, in contact on one side, and a little open at the 
other side, as in Fig. 16, p. 47. As the faces of the 
plates approach each other, the water rises higher, 
forming the curve, a. 

Capillary attraction performs many important offices 
in nature. The moisture of the soil depends greatly 
upon its action. If the soil is composed of coarse sand 
or gravel, the interstices are large, and, like the larger 
glass tube, will not retain the rain which falls upon it. 
Such soils are, therefore, easily worked in wet weather, 
but become too dry in seasons of drought ; but when 
the texture is finer, and especially if a due proportion 
of clay be mixed with the sand, the interstices become 
exceedingly small, and retain a full sufficiency of moist- 
ure. If, however, there is too much clay, the soil is 
apt to become close and compact, and the water can 
not enter until it is broken up or pulverized. It is for 
this reason that sub-soil plowing becomes so eminently 
beneficial, by deepening the mellow portion, and thus 
affording a larger reservoir, which acts like a sponge 
in holding the excess of falling rains, till wanted in the 
dry season. For the same reason, a well-cultivated 
soil is found to preserve its moisture much better dur- 
ing the heat of summer than a hardened and neglect- 
ed surface. 

If capillary attraction should cease to exist, the 
earth would soon become a barren and uninhabitable 
waste. The moisture of rains could not be retained 
by the particles of the soil, but would immediately 



ASCENT OF SAP. 49 

sink far down into the earth, leaving the surface at all 
times as dry and unproductive as a desert ; vegetation 
would cease ; brooks and rivers would lose the gradual 
supplies which the earth affords them through this in- 
fluence, and become dried up ; and all plants and all 
animals die for want of drink and nourishment. Thus 
the very existence of the whole human race evidently 
depends on a law, apparently insignificant to the un- 
thinking, but pointing the observing mind to a striking 
proof of the creative design which planned all the 
works of nature, and fitted them with the utmost ex- 
actness for the life and comfort of man. 

ASCENT OF SAP. 

The following interesting experiments serve to ex- 
plain the cause of the ascent of sap in plants and trees : 
Take a small bladder, or bag made of any similar 
fig- 17 - substance, and fasten it tightly on a tube 
open at both ends {Fig. 17) ; then fill them 
with alcohol up to the point C, and im- 
merse the bladder into a vessel of water. 
The alcohol will immediately rise slowly 
in the tube, and if not. more than two or 
three feet high, will run over the top. This 
is owing to the capillary attraction in the 
AvparatuTex- minute pores of the bladder, drawing the 

plaining the , .Vi .• ._ •• j» f .i ,i ■ 

rising of sap. water within it taster than the same at- 
traction draws the alcohol outward. One liquid will 
thus intrude itself into another with great force. A 
bladder filled with alcohol, with its neck tightly tied, 
will soon burst if plunged under water. If a bladder 
is filled with gum- water, and then immersed as before, 

C 




50 MECHANICS. 

the water will find its way within against a very heavy 
pressure. 

In this manner sap ascends through the minute tubes 
in the body of trees. The sap is thickened like gum- 
water when it reaches the leaves, and a fresh supply, 
therefore, enters through the pores in the spongelets of 
the roots by capillary attraction, and, rising through the 
stem, keeps up a constant supply for the wants of the 
growing tree. 



SECTION HI. 

CENTRE OF GRAVITY. 

The centre of gravity is that point in every hard 
substance or body, on every side of which the different 
parts exactly balance each other. If the body be a 
globe or round ball, the centre of gravity will be ex- 
actly at the centre of the globe ; if it be a rod of equal 
size, it will be at the middle of the rod. If a stone or 
any other substance rest on a point directly under the 
centre of gravity, it will remain balanced on this point ; 
but if the point be not under the centre of gravity, the 
stone will fall toward the heaviest side. 

Some curious experiments are performed by an in- 
genious management of the centre of gravity. A 
Fig 18 light cylinder of cork or 

pasteboard contains a con- 
cealed piece of lead, g 
(Figure 18). The lead, 
being heavier than the rest, 
will cause the cylinder to 
roll up an inclined plane, when placed as shown by the 




CENTRE OF GRAVITY. 



51 



Fig. 19. 




Fig. 20. 



lower figure on the preceding en- 
graving, until it makes half a revo- 
lution and reaches the place of the 
upper figure, when it will remain 
stationary. If a curved body, as 
shown in Fig. 19, be loaded heav- 
ily at its ends, it will rest on the 
stand, and present a singular ap- 
pearance by not falling, the cen- 
tre of gravity lying between the 
Body singularly balanced by two heavy portions on the end of 
the stand. A light stick of some 
length may be made to stand 
on the end of the finger, by 
sticking in two penknives, so 
as to bring the centre of grav- 
ity as low as the finger-end 
{Fig. 20). 

If any body, of whatever 
shape, be suspended by a hook 
or loop at its top, it will neces- 
sarily hang so that the centre 
of gravity shall be directly un- 
der the hook. In this way the 
centre in any substance, no 
matter how irregular its shape 
may be, is ascertained. Suppose, for 
instance, we have the irregular plate 
or board shown in the annexed figure 
(Fig. 21) : first hang it by the hook 
a, and the centre of gravity will be 
somewhere in the dotted line a b. 




Centre of gravity maintained by two 
penknives. 



Fig. 21. 




52 MECHANICS. 

Then hang it by the hook c, and it will be somewhere 
in the line c d. Now the point e, where they cross 
each other, is the only point in both, consequently this 
is the centre sought. If the mass or body, instead of 
being flat like a board, be shapeless like a stone or lump 
of chalk, holes bored from different suspending points 
directly downward will all cross each other exactly at 
the centre of gravity. 

LINE OF DIRECTION. 

An imaginary line from the centre of gravity perpen- 
dicularly downward to where the body rests is called 
the line of direction. 

Now in any solid body whatever, whether it be a 
wall, a stack of grain, or a loaded wagon, the line of 
direction must fall within the base or part resting upon 
the ground, or it will immediately be thrown over by 
its own weight. A heavily and evenly loaded wagon 
on a level road will be perfectly safe, because the line 
of direction falls equally between the wheels, as shown 

Fig. 22. Fig. 23. in Fig. 22, by the dotted 

•:""-"; : ,' " " line, c being the centre. But 

•■ C " \ f P ■' -c -j- 4. -J -un 

WmiWm W ■ s <&$^ v - P ass a stee P side-hill 

Lpl l/l v \k^\ road, throwing this line out- 

'f~ I T m >^0^ s ^ e ^ ie wnee l s > as m Fig: 
r*V"' , ' ESS *T" , '■ t^T ; j 23, it must be instantly 

Centre of gravity on level and inclined ' J 

roads - overturned. If, however, 

instead of the high load represented in the figure, it be 
some very heavy material, as brick or sand, so as not 
to be higher than the square box, the centre will be 
much lower down, or at b, and thus, the line falling 
within the wheels, the load will be safe from danger, 



LINE OF DIRECTION. 



53 



unless the upper wheel pass over a stone, or the lower 
wheel sink into a rut. The centre of gravity of a large 
load may be nearly ascertained by measuring with a 
rod ; and it may sometimes happen that by measuring 
the sideling slope of a road, all of which may be done 
in a few minutes, a teamster may save himself from a 
comfortless upsetting, and perhaps heavy loss. Again, 
a load may be temporarily placed so much toward one 
side, while passing a sideling road, as to throw the line 
of direction considerably more up hill than usual, and 
save the load, which may be adjusted again as soon 
as the dangerous point is passed. This principle also 
shows the reason why it is safer to place only light 
bundles of merchandise on the top of a stage-coach, 
while all heavier articles are to be down near the 
wheels ; and why a sleigh will be less likely to upset 
in a snow-drift, if all the passengers will sit or he on 
the bottom. "When it becomes necessary to build very 
large loads of hay, straw, wool, or other light sub- 
stances, the " reach," or the long connecting-bar of the 
wagon, must be made longer, so as to increase the 
length of the load ; for, by doubling the length, two 
tons may be piled upon the wagon with as much secu- 
rity from oversetting as one ton only on a short wagon. 

Where, however, a high 
load can not be avoided, 
great care must be taken 
to have it evenly placed. 
If, for instance, the load 
of hay represented by 
me-sided Figure 24 be skillfully 
built, the line of direc- 



Fig. 24. 



Fig. 25 




Centre of gravity of an even and one 
load. 



54 



MECHANICS. 



tion will fall equally distant within each wheel ; but a 
slight misplacement, as in Fig-. 25, p. 53, will so alter 
this line as to render it dangerous to drive except on a 
very even road. 

Thus every one who drives a wagon should under- 
stand the laws of nature sufficiently to know how to 
arrange the load he carries. It is true that experience 
and good judgment alone will he sufficient in many 
cases ; hut no person can fail to judge better, with the 
reasons clearly, accurately, distinctly before his eyes, 
than by loose conjecture and random guessing. 

Every farmer who erects a wall or building, every 
teamster who drives a heavy load, or even he who 
only carries a heavy weight upon his shoulder, may 
learn something useful by understanding the laws of 
gravity. 

It is familiar to every one, that a body resting upon 
a broad base is more difficult to overset than when the 
base is narrow. For instance, the square block (Fig". 
Fig. se. 26) is less easily thrown over than 

the tall and narrow block of equal 
weight, because, in turning the 
square block over its lower edge, 
the centre of gravity must be lift- 
ed up considerably in the curve 
shown by the dotted line c; but 
with a tall, narrow block, this 
curve being almost on a level, 
very little lifting is required. Hence the reason that 
a high load on a wagon is so much more easily over- 
turned than a low one. 

Of all forms, a pyramid stands the most firmly on its 




LINE OF DIRECTION. 



55 



Fig. 27. 




base. The centre of gravity, c (Fig. 26), being so 
near the broad bottom, it must be elevated in a very 
steep curve to throw the line of direction beyond the 
base. For this reason, a stone wall, or the dam for a 
stream, will stand better when broad at bottom and 
tapering to a narrow top than if of equal thickness 
throughout. 

When a globe or round ball is placed upon a smooth 
floor, it rests on a single point. If the floor be level, 
the line of direction will fall exactly 
at this resting-point (Fig. 27). To 
move the ball, the centre will move 
*•" precisely on a level, without being 
raised at all. This is the reason that 
- a ball, a cylinder, or a wheel is rolled 
forward so much more easily than any flat-sided or ir- 
regular body. In all these cases, the line of direction, 
although constantly changing its place, still continues 
to fall on the very point on which the round body rests. 
But if the level floor is exchanged for a slope or in- 
Fig 28 clined plane (Fig. 28), the line of 

direction no longer falls at the touch- 
ing-point, but on the side from it 
downward ; the ball will therefore, 
by its mere weight, commence roll- 
ing, and continue to do so till it 
reaches the bottom of the slope. 
Wheel-carriages owe their comparative ease of 
draught to the fact that the centre of gravity in the 
load is moved forward by the rolling of the wheels, on 
a level, or parallel with the surface of the road, just in 
the same way that the round ball rolls so easily. Bach 




56 



MECHANICS. 



Fig. 29. 



wheel supporting its part of the load at the hub, the 
same rule applies to each as to a ball or cylinder alone. 
Hence, on a level road, the line of direction falls pre- 
cisely where the wheels rest on the ground, but if the 
road ascend or descend, it falls elsewhere; this ex- 
plains the reason why it will run by its own weight 
down a slope. 

"Whenever a stone or other obstruction occurs in a 
road, it becomes requisite to raise the centre by the 
force of the team and by means of oblique motion, so 
as to throw the wheel over it, 
as shown by Fig-. 29. One 
of the reasons thus becomes 
very plain why a large wheel 
rig. 30. _ will run with 
more ease on 
a rough road 
than a small- 
er one ; the 

larger one mounting any stone or obstruction without 
lifting the load so much out of a level or direct line, as 
shown by the dotted lines in the annexed figures (Figs. 
29 and 30). Another reason is, the large wheel does 
Fig. 31. Fig. 32. not sink into the smaller 

cavities in the road. 

A self-supporting fruit- 
ladder (Figure 31) (the 
centre of gravity, when 
in use, being at or near 
the top) must have its 
m A dal^rmcs- legs more widely spread, 
'ladder.™ 1 ' to be secure from fall- 






A firmly-set fruit-ladder . 



LINE OF DIRECTION. 57 

ing, than if the centre were lower down. Hence such 
a position as in Fig. 32 would he unsafe. 

The support of the human body, in standing and 
walking, exhibits some interesting examples in rela- 
tion to this subject. A child can not learn to walk till 
he acquires skill enough to keep his feet always in the 
line of direction. "When he fails to do this, he topples 
over toward the side that the line falls outside his feet. 
A man standing with his heels touching the wash- 
board of a room can not possibly stoop over without 
falling, because, when he bends, the line of direction 
falls forward of his toes, the wall against which he 
stands preventing the movement of his body backward 
to preserve the balance. 

In walking, the centre rises and falls slightly at 
Fig. 33. each step, as shown by the waved line 

in Fig. 33. If it were not for the 
bending of the knee-joints, this exer- 
cise would be much more laborious, 
as it would then become needful to 
throw the centre into an upward curve 
at every step. For this reason, a wood- 
en leg is more imperfect than the nat- 
ural one (Fig. 34). Hence the reason 
why walking on crutches is laborious and fatiguing, 
because at every onward step the body must be thrown 
upward in a curve, like a wagon mounting repeated 
obstructions. 

"When a load is carried on the shoulder, it should be 

so placed that the line of direction may pass directly 

through the shoulder or back down to the feet, Fig. 

35, p. 58. An unskillful person will sometimes place 

C2 




58 



MECHANICS. 




Fig. 37 





Fig. 35. Fig. 36. a bag of grain as shown in Fig. 
36. The line falling outside his 
feet, he is compelled to draw 
downward with great force on 
the other end of the bag. A man 
who carries a heavy pole on his 
shoulder should see that the centre is directly over his 
shoulder, otherwise he will be compelled to bear down 
upon the lighter end, and thus add in an equal degree 
to the weight upon his body. 

If an elliptical or oval body, 
Fig. 37, rest upon its side a, roll- 
ing it in either direction elevates 
the centre, c, because it is nearest 

the side on which the body rests. 

If, when raised, it be suffered to 
fall, its momentum carries it be- 
yond the point of rest, and thus it 
continues rocking until the force is 
Fig. 38. spent. The course of the centre 

during these motions is shown 
by the curved dotted line, c. If 
it be placed upon end, as in Fig. 
38, then any motion toward ei- 
ther side brings the centre of 
gravity nearer the touching-point, 
that is, causes it to descend, and the body consequently 
falls over on its side. This may be easily illustrated 
with an egg, which will lie at rest upon its side, but 
falls when set on either end. 

The rockers of chairs, cradles, and cribs are formed 
on the principle just explained. If so made that the 





LINE OF DIRECTION. 



59 



centre of gravity of the chair or cradle is nearer the 
middle of the rocker than to the ends, the rocking mo- 
tion will take place ; and when the distance from the 
centre of gravity to the ends of the rockers is but little 



Fig. 39. 



Fig. 40. 




greater than the distance to the 
middle, c, as in Fig. 39, the mo- 
tion will be slow and gentle ; but 
if this difference be greater, as in 
Fig. 40, it will be rapid. "When 
the centre is high, the rockers must have less curvature 
than where it is low and near the floor. If the centre 
of gravity be nearer the ends than to the middle, the 
chair will immediately be overturned. This principle 
should be well understood in the construction of all in- 
struments which move by rocking. 



60 



MECHANICS. 



CHAPTER IV. 

SIMPLE MACHINES, OR MECHANICAL POWERS. 

SECTION" I. 
ADVANTAGES OF MACHINES. 

The moving forces which are applied to various use- 
ful purposes commonly require some change in veloc- 
ity, direction, or mode of acting before they accom- 
plish the desired end. For example, a running stream 
of water has a motion in one direction only ; by the 
use of machinery, we change this to an alternating mo- 
tion, as in the saw of the saw-mill, or to a rotatory or 
whirling motion, as in the stones of a grist-mill. The 
direct or straightforward power of a yoke of oxen is 
made, by the employment of the plow, to produce a 
side-motion to the sod as well as to turn it through 
half a circle. The thrashing-machine converts the 
slowly-acting pace of horses to the swift hum of the 
spiked cylinder. 

Any instrument used for thus changing or modify- 
ing motion is called a machine, whether it be simple 
or complex in its structure. Thus even a crowbar, 
used in lifting stones from the earth, by diminishing 
the motion given by the hand and increasing its power, 
may be strictly termed a machine ; while a harrow, 
which neither alters the course nor changes the veloci- 
ty of the force applied, may with more propriety be re- 
garded as simply an implement or tool. In common 



THE LAW OF VIRTUAL VELOCITIES. 61 

language, however, these distinctions are not accurate- 
ly observed, and a machine is usually considered to he 
any instrument consisting of different moving parts. 

All machines, however complex, may he resolved into 
two simple parts, or simple machines. These are, 

1. The Lever ; 

2. The Inclined Plane. 

The wheel and axle, and the pulley, are modified ap- 
plications of the lever ; and the wedge and the screw 
of the inclined plane, as will he shown on the follow- 
ing pages. These six are usually termed the mechan- 
ical powers. As they really do not possess any power 
in themselves, hut only regulate power, the term " sim- 
ple machines" may he regarded as most correct. 

THE LAW OF VIRTUAL VELOCITIES. 

Before proceeding to the simple machines, it may he 
well to explain a very important truth, which should he 
considered as lying at the foundation of all mechanical 
philosophy, and which renders plain and simple many 
things which would otherwise seem strange or contra- 
dictory. This is, that the force required to lift any 
given body is always in proportion to the weight of 
that body, taken together with the height to be raised. 
For instance, it requires twice the force to raise two 
pounds as to raise one pound, three times the force to 
raise three pounds, and so forth. Also, twice as great 
a force is needed to elevate any weight two feet as one 
foot, or three times as great for three feet, and so on. 
Again, combining these together, four times as great a 
force is required to raise two pounds to a height of two 
feet as to raise one pound only one foot ; eight times 



62 MECHANICS. 

as great for four feet, and so on. This holds true, no 
matter by what kind of machinery it is accomplished. 
Now this may all seem very simple, but it serves to ex- 
plain many difficult questions in relation to the real 
power possessed by all machines. 

Take another example. Suppose that one wishes to 
raise a weight of 1000 pounds to a height of one foot. 
If his strength is only equal to 100 pounds, the weight 
would be ten times too heavy for him. He might, 
therefore, divide it into ten equal parts of 100 pounds 
each. Raising each part separately the required height 
of one foot, would be the same as raising one of them 
ten feet high. The weight is lessened ten times, but 
the distance is increased ten times. But there are 
some bodies, as, for example, blocks of stone or sticks 
of timber, which can not well be divided into parts in 
actual practice. He therefore resorts to a machine or 
mechanical power, through which the same result is 
accomplished by raising the whole weight in one mass 
with his single strength ; but in this case as well as 
the other, the moving force which he applies must pass 
through ten times the space of the weight. "We arrive, 
therefore, at the general rule, that the distance moved 
by the weight is as much less than that moved by the 
power as the power is less than the weight. This rule 
is termed by some writers the " rule of virtual veloc- 
ities" virtual meaning not apparent or actual, but 
according to the real effect, because the increase in 
the velocity of the power makes up for increase in the 
size of weight. This rule will be better understood 
after considering its application to the different simple 
machines. 



THE LEVER. 63 

SECTION" II. 
THE LEVER.. 

The simplest of all machines is the lever. It con- 
sists of a rod or bar, one end resting upon a prop ox ful- 
crum, F {Fig. 41), near which is the weight, W, moved 

Fig. 41. 



Lever of the second kind. 

by the hand at P. The stone may weigh 1000 pounds ; 
yet, if it is ten times as near the fulcrum as the man's 
hand is, a force of 100 pounds will lift it ; but it will 
be moved only a tenth part as high as the hand has 
been moved, as shown by the dotted lines. By placing 
the stone still nearer the fulcrum, still less will be the 
power required to raise it, but then the distance ele- 
vated would be also still less. By sufficiently increas- 
ing the disproportion between the two parts of the le- 
ver, the strength of a child merely might be made to 
move more than many horses could draw. 

These performances of the lever often excite aston- 
ishment at what appears to be out of the common 
course of things ; yet, when examined by the princi- 
ples of mechanics, instead of appearing matters of as- 
tonishment, they are found to be only the natural and 
necessary results of the laws of force. In the case of 
the lever just described, it is often incorrectly supposed 
that the power itself sustains the weight. But this is 



64 MECHANICS. 

not the case ; nearly the whole of it rests upon the ful- 
crum. We often see proofs of this error in common 
practice, where fulcrums or props entirely insufficient 
to uphold the enormous weight to be raised are at- 
tempted to be used. If the weight, for instance, be 
ten times as near the fulcrum as to the power, then 
nine tenths of the weight rests upon the fulcrum, and 
the remaining tenth only is sustained by the lifting 
power. The lever only allows the power to expend it- 
self through a longer distance, and thus, by concentra- 
ting itself at the weight, to elevate the latter through 
the shorter distance, according to the rule of virtual 
velocities already explained. 

The fulcrum may be placed between the weight and 
Fig. 42. the power, as in 

Sb Fi Z- 42 ' or the 

** iS3aa ' power may be 

Lever of the first kind. placed between 

Fig. 43. the fulcrum and the 

weight, as in Fig. 

SJ^— 43, the same princi- 



Lever of the third hind. ^ q£ ^^ yeloci _ 

ties applying in all cases. 

Where the fulcrum is between the power and the 
weight, as in Fig. 42, it is called a lever of the first 
kind. 

Where the weight is between the fulcrum and the 
power, as in Fig. 41, it constitutes a lever of the 
second kind. 

Where the power is between the fulcrum and the 
weight, as in Fig. 43, it is termed a lever of the third 
kind. 



THE LEVER. 65 

1. Many examples occur in practice of levers of the 
first kind. A crowbar, used to raise stones from the 
earth, is an instance of this sort ; so is a handspike of 
any kind used in the same way. A hammer for draw- 
ing a nail operates as a lever of the first kind, the heel 
being the fulcrum, the nail the weight, and the hand 
the power; the distance through which the handle 
passes being several times greater than that of the 
claws, the force exerted on the nail is increased in like 
proportion. A pair of scissors consists of two levers, 
the rivet being the fulcrum ; and in using them, as ev- 
ery one has observed, a greater cutting force is exert- 
ed near the rivets than toward the points. This is ow- 
ing to the power being expended through a greater dis- 
tance near the points, according to the rule already 
explained. Pincers, nippers, and other similar instru- 
ments are also double levers of the first kind. 

A common steelyard is another example, the sliding 
weight becoming gradually more effective as it is moved 
further from the fulcrum or hook supporting the instru- 
ment. The brake or handle of a pump is a lever of 
this class, the pump-rod, and piston being the weight. 
The common balance is still another, the two arms 
being exactly equal, so that 
one weight will always bal- 
ance the other, and on this 
its usefulness and accuracy 
entirely depends. The most 
sensitive balances have light 
beams with long arms, and 
the turning-point of hardened steel or agate, in the 
form of a thin wedge, on which the balance turns al- 




66 



MECHANICS. 



most without friction. Small balances have been so 
skillfully constructed as to turn with one thousandth 
part of a grain. 

2. Levers of the second kind are less numerous, but 
not uncommon. A handspike used for rolling a log is 
an example. A wheel-barrow is a lever of the second 
kind, the fulcrum being the point where the wheel rests 
on the ground, and the weight the centre of gravity of 
the load. Hence, less exertion of strength is required 
in the arm when the load is placed near the wheel, 
except where the ground is soft or muddy, when it is 
found advantageous to place the load so that the arm 
shall sustain a considerable portion, to prevent the 
wheel sinking into the soil. A two-wheeled cart is a 
similar example ; and, for the same reason, when the 
ground is soft, the load should be placed forward to- 
ward the horse or oxen ; on the other hand, on a smooth 
and hard, or on a plank road, the load should be more 
nearly balanced. An observance of this rule would 
often save a great deal of needless waste of strength. 
A sack-barrow, used in barns and mills for convey- 
Fig. 45. ing heavy bags of grain from one 

part of the floor to another, is a le- 
ver nearly intermediate between 
the first and second kind, the 
weight usually resting very near- 
ly over the fulcrum or wheels. 
When the bag of grain is thrown 
forward of the wheels, it becomes 
a lever of the first kind ; when 
back of the wheels, it is a lever 
sack-barrow. f the second kind. As it is 




ESTIMATING THE POWER OF LEVERS. 67 

used only on hard and smooth floors, and not, like the 
wheel-harrow, on soft earth, the more nearly the load 
is placed directly over the wheels, the more easily they 
will run. 

3. In a lever of the third kind, the weight being 
further from the fulcrum than the power, it is only 
used where great power is of secondary importance 
when compared with rapidity and dispatch. A hand- 
hoe is of this class, the left hand acting as the fulcrum, 
the right hand as the power, and the resistance over- 
come by the blade of the hoe as the weight. A hand- 
rake is similar, as well as a fork used for pitching hay. 
Tongs are double levers of this kind, as also the shears 
used in shearing sheep. The limbs of animals, gener- 
ally, are levers of the third kind. The joint of the bone 
is the fulcrum ; the strong muscle or tendon attached 
to the bone near the joint is the power ; and the weight 
of the limb, with whatever resistance it overcomes, is 
the weight. A great advantage results from this con- 
trivance, because a slight contraction of the muscle 
gives a swift motion to the limb, so important in walk- 
ing and running, and in the use of the arms. 



SECTION HI. 

ESTIMATING THE POWER OF LEVERS. 

The power of any lever is easily calculated by meas- 
Fig- 46. uring the length of 

-"'-'■ kfo ^ S ^ W ° armS 5 ^ a ^ 

w is, the two parts in- 
to which it is divi- 

Lever of the first kind. ded by the Weight, 



-C^--:-- 



68 MECHANICS. 

fulcrum, and power. In a lever of the first kind, if 
the weight and power be equally distant from the ful- 
crum, they will move through equal distances, and 
nothing will be gained ; that is, a power of 100 pounds 
will lift a weight of 100 pounds only. If the power be 
Fig. 47. twice as far as the 

7 "" -'--::,..._ weight, its force 

will be doubled ; 

if three times, it 
\ F will be tripled ; 



w 

Lever of the second kind. and SO forth. Ill 

a lever of the second kind, if the weight be equidistant 
between the fulcrum and power, the power will move 
through twice the distance of the weight, and the pow- 
er of the instrument will therefore be doubled ; if twice 
as far, it will be tripled, and so on, as shown in the an- 
nexed figures. The same mode of reasoning will ex- 
plain precisely to what extent the force is diminished 
in levers of the third kind. 

These rules will show in what manner a load borne 
on a pole is to be placed between two persons carrying 
it. If equidistant between them, each will sustain a 
like portion. If the load be twice as near to one as to 
the other, the shorter end will receive double the weight 
of the longer. For the same reason, when three horses 
are worked abreast, the two horses placed together 
should have only half the length of arm of the main 
whipple-tree as the single horse, Fig. 48. The farmer 
who has a team of two horses unlike in strength, may 
thus easily know how to adjust the arms of the whip- 
ple-tree so as to correspond with the strength of each. 
If, for instance, one of the horses possesses a strength 



ESTIMATING THE POWER OF LEVERS. 

Fig. 48. 



69 




as much greater than the other as four is to three, 
then the weaker horse should be attached to the arm 
of the whipple-tree made as much longer than the oth- 
er arm as four is to three. 

In all the preceding estimates, the influence of the 
weight of the lever has not been taken into consider- 
ation. In a lever of the first kind, if the thickness of 
the two arms he so adjusted that it will remain bal- 
anced on the fulcrum, its weight will have no other 
effect than to increase the pressure on the fulcrum ; 
but if it be of equal size throughout, its longer arm, 
being the heaviest, will add to its power. The amount 
thus added will be equal to the excess in the weight 
of this arm, applied so far along as the centre of grav- 
ity of this excess. If, for example, a piece of scantling 

twelve feet long, 
a b, Fig: 49, be 
used as a lever to 
lift the corner of 
a building, then 
the two portions, a c, c d, will mutually balance each 
other. If these be each a foot in length, the weight of 
ten feet will be left to bear down the lever. The cen- 



Fig. 49. 




70 MECHANICS. 

tre of gravity of this portion will be at e, six feet from 
the fulcrum,' and it will consequently exert a force un- 
der the building equal to six times its own weight. 
If the scantling weigh five pounds to the foot, or fifty 
pounds for the excess, this force will be equal to three 
hundred pounds. 

In the lever of the second kind, its weight operates 
against the moving power. If it be of equal size 
throughout, this will be equal to just one half the 
weight of the lever, the other half being supported by 
the fulcrum. 

With the lever of the third kind, the rule applied to 
the first must be exactly reversed. 

COMBINATION OF LEVERS. 

A great power may be attained without the incon- 
venience of resorting to a very long lever, by means of 
Fi 50 a combination of levers. 

i ; n , $ In Fig. 50, the small 

&"• i #\ ; ffiJk weight P, acting as a 

r r W • , 

movmg power, exerts a 
three-fold force on the next lever ; this, in its turn, acts 
in the same degree on the third, which again increases 
the power three times. Consequently, the moving 
power, P, acts upon the weight, W, in a twenty-seven- 
fold degree, the former passing through a space twen- 
ty-seven times as great as the latter. 

A combination of levers like this is employed in self- 
regulating stoves. It is in this case, however, used to 
multiply instead of to diminish motion. The expan- 
sion "of a metallic rod by heat the hundredth part of an 
inch acts on a set of iron levers, and the motion is in- 



WEIGHING MACHINE. 



71 



creased, by the time it reaches the draught-valve, to 
about one hundred times. 

A more compact arrangement of compound levers 
is shown in Fig. 51, where the power, P, acts on 

the lever A, exerting a force 
on the lever B five times as 
great as the power. B acts 
on the lever C with a force 
increased three times, and 
this, again, on the weight, 
"W, with a four-fold force. 
Multiplying 5, 3, and 4 to- 
gether, the product is 60 ; 
hence a force of one pound 
at P will support 60 pounds 
| at W. By graduating (or 
marking into notches) the le- 
ver C, so that the distance is measured as the weight 
is moved along it, a compact and powerful steelyard for 
weighing is formed. 




WEIGHING MACHINE. 



A valuable combination of levers is made in the con- 
struction of the weighing machine, used for weighing 

Fig. 52. 




Weighing Machine. 



72 MECHANICS. 

cattle, wagons loaded with hay, and other heavy arti- 
cles. The wagon rests on the platform A {Fig. 52, 
p. 71), and tins platform rests on two levers at W, W, 
which presses their other ends both on a central point, 
and this again hears on the lever D, the other end of 
which is connected by means of an upright rod with 
the steelyard at F. 

There are two important points gained in this com- 
bination. In the first place, the levers multiply the 
power so much that a few pounds' weight will balance 
a heavy load of hay weighing a ton or more ; and, in 
the next, the load resting on both the levers, commu- 
nicates the same force of weight to the central point, 
from whatever part of the platform it happens to stand 
on ; for if it presses hardest on one lever, it bears light- 
er, at a corresponding rate, on the other. In practice, 
there are always two pairs, or four levers, which pro- 
ceed from each corner of the platform, and rest on one 
point at the centre. "VVe have taken the two only, to 
simplify the explanation. 

STUMP MACHINES. 

A simple contrivance for allowing a succession of 
efforts in the use of the lever is represented in the ac- 
companying figure {Fig. 53), and is used for tearing 
out the roots of partly decayed stumps. It may be 
also applied to lifting heavy weights, and to various 
other purposes. Two pieces of strong, three-inch white- 
oak plank, eight inches wide and seven feet long, are 
connected at the ends, and are furnished with the 
movable leg, d. Two rows of holes are bored through 
them, to receive iron pins, which are to serve as ful- 



STUMP MACHINE. 
Fig. 53. 



73 





Fig. 54. crams. A strong lever, a, is furnish- 
ied at one end with a thick iron hook 
(shown in Fig. 54), which is first fast- 
ened on the root of the stump, and then 
one of the pins is inserted under the 
lever. The lever is now elevated, and 
the other holt is placed under it. It is 
next pressed down, and the first bolt 
elevated one hole higher, and so on till 
the stump is torn out. To prevent the lever slipping, 
a notch is made in its under side, on each side of the 
hook, as shown in Fig. 54. 

A more powerful stump-extracting machine, made 
on precisely the same principle, is exhibited by Fig. 
55, p. 74. The lever, a, should be a strong stiok of 
timber, furnished with three massive iron hooks, se- 
cured by bolts passing through, as represented in the 
figure. Small or truck wheels are placed at each end 
of the lever, merely for the purpose of moving it easily 
over the ground. The stump, b, used as a fulcrum, 
has the chain passing round near its base, while an- 
other chain passes over the top of the stump, c, to be 
torn out. A horse is attached to the lever at d, and, 
moving to e, draws the other end of the lever back- 



74 



MECHANICS. 
Fig.' 55. 




ward, and loosens the stump ; while in this position, 
another chain is made to connect g to A, and the horse 
is turned about, and draws the lever backward to i, 
which still further increases the loosening ; a few rep- 
etitions of this alternating process tears out the stump. 
Very strong chains are requisite for this purpose. 
Large stumps may require an additional horse or a 
yoke of oxen. Where the stumps are remote from 
each other, iron rods with hooks may be used to con- 
nect the chains. 

The power which may be given to this and to all 
other modes of using the lever, as we have already 
seen, depends on the difference between the lengths of 
its two arms. A yoke of oxen, drawing with a force 
of 500 pounds on the long arm of a lever 25 feet long, 
will exert a force on the short arm of six inches equal 



WHEEL AND AXLE. 75 

to 50 times 500 pounds, or 25,000 pounds, on the 
stump. 

It was after an examination of the great power 
which may be given to the lever by increasing this dif- 
ference that Archimedes exultingly exclaimed, " Give 
me but a fulcrum whereon to place my lever, and I 
will move the earth !" Admitting the theoretical truth 
of this exclamation, and supposing there could be a 
lever which he might have used for this purpose, its 
practical impossibility may be quickly understood by 
computing the whole bulk of the globe ; for such is 
its enormous size and cubical contents, that Archim- 
edes must have moved forward his lever with the 
strength of a hundred pounds and the swiftness of a 
cannon ball for eight hundred million years to have 
moved the earth the thousandth part of an inch ! 



SECTION rv. 

WHEEL AND AXLE. 

In treating of the lever, it was shown to be capa- 
ble of exerting a force through a small distance only. 
Hence, if a heavy body were required to be elevated 
to any considerable height, it would be necessary to 
accomplish it by a succession of efforts. This incon- 
venience is removed by a constant and unremitted 
action of the lever in the form of the wheel and axle. 

Let the weight, w (Fig. 56, p. 76), be suspended by 
a cord from the end of the lever, a b, and a wheel at- 
tached to the lever, so that this cord may wind upon 
it as the weight is elevated ; then let the power be ap- 
plied at the other end by means of a cord, and a larger 



76 



MECHANICS. 




Fig. 56. wheel be attached, so that 

this cord too may wind upon 
the larger wheel. These two 
wheels (fastened together so 
>* as to form one), as they are 
made to revolve on their axis, 
will now constitute, in a man- 
ner, a succession of levers, act- 
ing through an indefinite dis- 
tance according to the length 
of the cords. The levers here 
successively acting are of the 
"first kind," and the axis of 
the wheel is the fulcrum. This arrangement consti- 
tutes in substance the wheel and axle ; and its power, 
like that of the simple lever, depends on the compara- 
tive velocity of the weight and the moving force. If, 
for example, the larger wheel is four times the circum- 
ference of the smaller, a force of one hundred applied 
to the outer cord will raise a weight of four hundred 
pounds. 

The annexed figure exhibits at one view the pow- 
er exerted through 
the wheel and axle, 
where a small weight 
of 6 pounds will wind 
up (or balance) oth- 
er weights separate- 
ly, weighing 8, 12, 
or 24 pounds, as the 
difference increases 
between the size of 



Fig. 57. 




Wheel and axle, showing the heavier weight for 



WHEEL AND AXLE. 77 

the wheel and of the axle, according to the rule of vir- 
tual velocities already explained. 

The thickness of the rope has not been taken into 
consideration. This is very small when compared with 
the diameter of the outer wheel, but often considerable 
when compared with that of the inner. To be strictly 
accurate, therefore, the force must be considered as act- 
ing at the centre of the rope ; hence the diameter of 
the rope must be added to the diameter of the wheel. 

There are various forms of the wheel and axle. In 
the common windlass, motion is given to the axle by 
means of a winch, which is a lever like the handle of 
a grindstone. The windlass used in digging wells 
has usually four projecting levers or arms. The wheel 
used in steering a vessel is furnished with pins in the 
circumference, to which the hand is applied in turning 
it. In the capstan (for weighing anchor) the axis is 
vertical, and horizontal levers are applied around it, so 
that several men may work at once. The power of 
all these forms is easily calculated by the rule of vir- 
tual velocities — that is, that the velocity with which 
the power moves is as many times greater than the ve- 
locity of the weight, as the weight exceeds the power. 
A simple and convenient rule for computing in num- 
bers the power of wheel- work is the following : Multi- 
ply all the numbers together which express either the 
circumferences or diameters of the large wheels, and 
then multiply together all the numbers which express 
the diameters of the smaller wheels or pinions ; divide 
the greater number by the lesser, and the quotient will 
be the power sought. 



78 



MECHANICS. 



MOLE PLOW. 



A good example of the power of the wheel and axle 
is furnished in the English Mole Plow for draining 
land (Fig-. 58). It has a wooden "beam, sheathed with 




BAND AND COG WHEELS. 



79 



iron on the lower side, which moves close to the ground, 
below which a thin, broad coulter extends downward, 
and to the lower end of this coulter a sharp iron cylin- 
der is attached. This moves horizontally, point fore- 
most, through the soil, producing a hollow channel be- 
neath the plow for the escape of the water, the only 
trace on the surface being a narrow slit left by the 
coulter. It is dragged forward by means of a chain 
and capstan worked by a horse, the machine itself be- 
ing fixed with strong iron anchors. This mode of 
draining is only adapted to clay soil, and is very cheap- 
ly performed, but is now little used since the introduc- 
tion of tile-draining. Fowler's Draining Plow, de- 
scribed hereafter, is a great improvement on the mole 
plow, and draws the tile-tubing into the channel as 
fast as it is made, forming a perfect drain by one op- 
eration. 



BAND AND COG WHEELS. 

Where great power is required, several wheels and 
axles may be combined in a manner corresponding 
with that of the compound system of levers already 
explained. In this case, the axis of one wheel acts on 
the circumference of the next, producing a continued 
slower motion, and increasing the power in a corre- 
Fig. 59. sponding degree. The wheels 

are made thus to act by means 
of cogs or teeth, or of bands 
{Fig. 59). In ordinary prac- 
tice, however, combined wheels 
are made use of to multiply 
combined cog-wheeis. motion instead of to diminish 




80 



MECHANICS. 



it, familiar instances of which occur in the grist-mill 
and thrashing-machine. 

In connecting a system of wheels, the cord or strap 
may he used where great force is not required, the 
friction round the circumference heing sufficient to pre- 
vent slipping. Bands are chiefly useful where motion 
is to he transmitted to a distance ; as, for example, 
from a horse-power without a ham to a thrashing-ma- 
chine within it. Liability of sliding is sometimes use- 
ful, by preventing the machinery from breaking when 
a sudden obstruction occurs. Where the force is great, 
the necessary tension or tightness of the cord produces 
too great a friction at the axle. In such cases, cogs or 
teeth must be resorted to. 

The term teeth is usually applied when they are 
formed of the same piece as the wheel, as in the case 
of cast-iron wheels. Cogs are teeth formed separate- 
ly and inserted into the wheel, as with wooden wheels. 
Pinions are the small wheels, or, more properly, teeth 

set on axles. 



Fig. 60. 




Form of cogs — a, badly 
formed; b, proper form. 



FORM OF TEETH OR COGS. 

The form of the teeth 
has a great influence on 
the amount of friction 
among wheel- work. Bad- 
ly-formed teeth are repre- 
sented by the wheel- work 
at a, in the annexed fig- 
ure, consisting of square 
projecting pins. "When 
these teeth first come into 



FORM OF TEETH OR COGS. 



81 



contact with each other, they act obliquely together, 
and thus a part of their force is lost, and they continue 
scraping together with a large amount of friction so 
long as they remain in contact. These effects are 
avoided by giving to them the curved form represented 
by b. Here, instead of pressing each other obliquely, 
they act at right angles, that is, not obliquely ; and in- 
stead of scraping, they roll over each other with ease. 
These curves are ascertained by mathematical calcu- 
lation, which can not be here given ; it may be enough 
to state that they should be so formed that the points 
in contact shall always work at right angles to each 
other. For ordinary practical purposes, however, they 
Fig. 6i. may be made as is 

shown in the annex- 
k _ ed figure {Fig. 61), 
by striking circles 
whose diameter shall 
embrace just three 
teeth. The points of 
the teeth thus form- 
Mode of giving the best/orm to cogs. ed are removed, leav- 
ing a blunt extremity, according to. the figure. 

There are a few other rules that should always be 
observed in constructing wheel-work, in order that the 
wheels may run easily together, without jerking or 
rattling, the most important of which are the follow- 
ing: 

1. The teeth must be of uniform size and distance 
from each other, through the whole circumference of 
the wheel. 

2. Any tooth must begin to act at the same instant 

D2 




82 MECHANICS. 

that the preceding tooth ceases to touch its correspond- 
ing tooth on the other wheel. 

3. There must be sufficient space between the teeth 
not only to admit those of the other wheel, but to al- 
low a certain degree of play, which should be equal to 
at least one tenth of the thickness of the teeth. 

4. The pinions should not be very small, unless the 
wheels they act on are quite large. In a pinion that 
has only eight teeth, each tooth begins to act before it 
reaches the line of the centres, and it is not disengaged 
as soon as the next one begins to act. A pinion of ten 
teeth will not operate perfectly if working in a wheel 
of less than 72 teeth. Pinions of less than six teeth 
should never be used. 

5. To give strength to the teeth of wheels, make the 
wheels themselves thicker, which increases the breadth 
of the teeth. 

6. Wheel- work is often defective in consequence of 
the relative number of teeth working together not be- 
ing such as to equalize the wear of all alike. If the num- 
ber of teeth on a wheel is divided without a remainder 
by the number of the pinion, then the same teeth will 
repeatedly engage each other, and they will often wear 
unevenly. The number should be so arranged that 
every tooth of the pinion may work in succession into 
the teeth of the wheel. This is best effected by first 
taking a number for the wheel that will be evenly di- 
vided by the number on the pinion, and then adding 
one more tooth to the wheel. This will effect a contin- 
ual change, so that no two shall be engaged with each 
other twice until all the rest have been gone through 
with. This odd tooth is called the hunting-cog. 



THE PULLEY. 



83 




Cog-wheels are most usually made with the teeth 
on the outside or circumference of the wheel ; these 
are termed spur-wheels. If the teeth are set on one 
side of the wheels, they are termed crown- 
wheels. "When they are made so as to 
i work together obliquely, they are called 
bevel-wheels, as in Fig. 62. pig. 63. 

Where the obliquity isi 
small, the motion may be 
communicated by means of the univer- 
sal joint, as shown in Fig. 63. This is 
commonly used in the thrashing-ma- 
chine, where there is a slight change 
in the direction of motion between the 
horse-power and the thrasher. /; " lverml ■" H,u 



Bevel-wheels. 




SECTION V. 



THE PULLEY. 



Let a cord fixed at one end pass round a movable 
grooved wheel, and be grasped by the hand at the other 
Fig. 64. en( j • then, in lifting any weight attach- 
ed to the wheel, by drawing up the cord, 
the hand will move with twice the ve- 
locity of the weight. It will, therefore, 
exert double the degree of force. This 
operates precisely as a succession of le- 
vers of the second kind, the fixed cord 
being the fulcrum, and the cord drawn 
up by the hand the power. It thus con- 
stitutes one of the simplest kinds of the 

Pulley doubling the ,. _,. n . 

force. pulley, tig. 64. 




84 



MECHANICS. 



The wheel is called a sheave; the term pulley is 
Fig. 65. applied to the block and sheave ; and a 
combination of sheaves, blocks, and ropes 
is called a tackle. 

There are various combinations of sin- 
gle pulleys for increasing power, the most 
common of which, and least liable to be- 
come deranged by the cord being thrown 
off the wheels, is shown in Fig. 65. In 
this and in all similarly constructed pul- 
leys, the weight is as many times great- 
er than the power as the number of cords 
which support the lower block. If there 
be six cords, as in F te- 66 - 

the figure, the weight 
will be six times the 
power. 

Where a cord is 
passed over a single fixed wheel, 
as in Fig. 66, or over two or more 
wheels, as in Fig. 67, no power is 
gained, the moving force being the 
same in velocity as the weight. 
Such pulleys are sometimes, how- 
ever, of use by altering the direc- 
tion of the force. The latter is 

"• _ . Pulley with no increase of 

applied with advantage to unload- power. 

ing or pitching hay by means of a horse power, saving 
much time and labor, as shown in Fig. 67. The head 
of the fork (Fig. 68) is about 28 inches long, and is 
fitted with steel prongs 20 inches long. The rope at- 
tached at a passes over the pulley above, by which the 





Pulley of six-fold 
power. 



THE PULLEY. 



85 



Fig. 67. 



Fig. 68. 




Pitching hay with horse-power. 

fork, after "being thrust into the hay, is lifted by the 
strength of the horse working just without the barn 
door. It is kept level by means of the rope, b, until the 
fork is high enough to unload, when this rope is slack- 
ened, and the hay deposited. The man on the mow 
can give any direction to the hay he pleases while it 
remains suspended. The horse is backed, and the op- 
eration repeated. The arrangement is cheap, and with 
it six tons have been pitched 20 feet high in an hour. 
The usefulness of the pulley depends mainly upon 
its lightness and portable form, and the facility with 
which it may be made to operate in almost any situ- 
ation. Hence it is much used in building, and is ex- 
tensively applied in the rigging of ships. In the com- 
putation of its power there is a large drawback, not 
taken into account in the preceding calculation, which 
materially lessens its advantage ; this is the friction of 



86 MECHANICS. 

the wheels and blocks and the stiffness of the cordage, 
which are often so great that two thirds of the power 
is lost. 



SECTION VI. 
THE INCLINED PLANE. 




The inclined plane or slope possesses a power which 
is estimated by the proportion which its length bears 
to the height. If, for example, the plane be twice as 
Fi 69 long as the perpendicular height, 

then in rolling the body, #, up 
the inclined plane (Fig: 69), it 
will move through twice the dis- 
tance required to lift it directly 
from b to c. Therefore only one half the strength else 
required need be exerted for this purpose. The same 
reasoning will apply to any other proportion between 
the height and length; that is, the more gradual or 
less steep the slope becomes, the greater will be the 
advantage gained. A familiar example occurs in lift- 
ing a loaded barrel into a wagon : the longer the plank 
used in rolling it, the less is the exertion needed. 

A body, in rolling freely down an inclined plane, ac- 
quires the same velocity that it would attain if dropped 
perpendicularly from a height equal to the perpendic- 
ular height of the plane. Thus, if an inclined plane 
on a plank road be 100 yards long and 16 feet high, a 
freely running wagon, left to descend of its own accord, 
will move 32 feet per second by the time it reaches 
the bottom, that being the velocity of a stone falling 
16 feet. Or, a rail-car on an inclined plane 145 feet 



ASCENT IN ROADS. 87 

high will attain a speed of 96 feet per second, or more 
than 65 miles an hour, at the foot of the plane, which 
is equal to the velocity of a stone falling three seconds, 
or 145 feet. 

ASCENT IN ROADS. 

All roads not perfectly level may be regarded as in- 
clined planes. By the application of the preceding 
rule, we may discover precisely how much strength is 
lost in drawing heavy wagons up hill. If the load 
and wagon weigh a ton, and the road rise one foot in 
height to every five feet of distance, then the increased 
strength required to draw the load will he one fifth of 
its weight, or equal to 400 pounds. If it rise only one 
foot in twenty, then the increase in power needed to 
ascend this plane will be only 100 pounds. The great 
importance of preserving as nearly as practicable a per- 
fect level is very obvious. 

There are many roads made in this country, rising 
over and descending hills, which might be made near- 
ly level by deviating a little to the right or to the left. 
Suppose, for example, that a road be required to con- 
nect the two points a and b {Fig. 70), three miles 



apart, but separated by a lofty hill midway between 
them, and one mile in diameter. Passing half a mile 
on either side would entirely avoid the hill, and the 
road thus curved would be only one hundred and forty- 



88 MECHANICS. 

eight yards, or one twelfth of a mile longer. The same 
steep hill is ascended perhaps fifty to five hundred times 
a year by a hundred different farmers, expending an 
amount of strength, in the aggregate, sufficient to ele- 
vate ten thousand tons annually to this height, as a 
calculation will at once show — more than enough for 
all the increased expense of making the road level. 

It is interesting and important to examine how 
much further it is expedient to carry a road through 
a circuitous level course than over a hill. To ascer- 
tain this point, we must take into view the resistance 
occasioned by the rough surface or soft material of the 
road. Roads vary greatly in this particular, but the 
following may be considered as about a fab; average. 
In drawing a ton weight (including wagon) on freely 
running wheels, on a perfect level, the strength exert- 
ed will be found about equal to the following : 

On a hard, smooth plank road 40 pounds. 

On a good Macadam road 60 " 

On a common good hard road 100 " 

On a soft road about 200 " 

Now let us compare this resistance to the resistance 
of drawing up hill. First, for the plank road — forty 
pounds is one fiftieth of a ton ; therefore a rise of one 
foot in fifty of length will increase the draught equal 
to the resistance of the road. Hence the road might 
be increased fifty feet in length to avoid an ascent of 
one foot ; or, at the same rate, it might be increased a 
mile in length to avoid an ascent of one hundred and 
five feet. But in this estimate the increase in cost of 
making the longer road is not taken into account. If 
making and keeping in repair be equal to three hund- 



ASCENT IN ROADS. 89 

red dollars yearly per mile, and one hundred teams 
pass over it daily, at a cost for traveling of four cents 
each per mile, being four dollars daily, or twelve hund- 
red dollars per annum, then the cost of making and re- 
pair would be one quarter of the expense of traveling 
over it. Therefore the mile should be diminished one 
quarter in length to make these two sources of expense 
counterbalance each other. Hence a road with this 
amount of travel should, with a reference to public ac- 
commodation, be made three fourths of a mile longer 
to avoid a hill of one hundred and five feet. This es- 
timate applies to loaded teams only. For light car- 
riages the advantages of the level road would not be 
so great. One half to five eighths of a mile would, 
therefore, be a fair estimate for all kinds of traveling 
taken together. 

The following table shows the rise in a mile of road 
for different ascents : 

For a rise of 1 foot in 10, the road ascends 528 feet per mile, 
do. 1 do. 13, do. 406 do. 



do. 


1 


do. 


15, 


do. 


352 


do. 


do. 


1 


do. 


20, 


do. 


264 


do. 


do. 


1 


do. 


25, 


. do. 


211 


do. 


do. 


1 


do. 


30, 


do. 


• 1T6 


do. 


do. 


1 


do. 


35, 


do. 


151 


do. 


do. 


1 


do. 


40, 


do. 


132 


do. 


do. 


1 


do. 


45, 


do. 


111 


do. 


do. 


1 


do. 


50, 


do. 


106 


do. 


do. 


1 


do. 


100, 


do. 


53 


do. 


do. 


1 


do. 


125, 


do. 


42 


do. 



The same kind of reasoning applied to a common 
good road will show that it will be profitable for the 
public to travel about half that distance to avoid a hill 
of one hundred and five feet. In this case the whole 



90 MECHANICS. 

yearly cost of the road, including interest on the land, 
and the cost of repairs, would not usually he more 
than a tenth part of the same cost for plank, or would 
not exceed thirty dollars. 

On rail-roads, where the resistance is only ahout one 
fifth part of the resistance of plank roads, the dispro- 
portion between the draught on a level and up an as- 
cent becomes many times greater. Thus, if a single 
engine will move three hundred and fifty tons on a lev- 
el, then two engines will be required for an ascent of 
only twenty feet per mile, four engines for fifty feet per 
mile, and six engines for eighty feet per mile. 

Such estimates as these merit the attention of the 
farmer in laying out his own private farm roads. It 
may be worthy of considerable effort to avoid a hill of 
ten or twenty feet, which must be passed over a hund- 
red times yearly with loads of manure, grain, hay, and 
wood. The greatly-increased resistance of soft mate- 
rials, also, is too rarely taken into account. A few 
loads of gravel, well applied, would often prevent ten 
times the labor in plowing through deep ruts, to say 
nothing of the breaking of harness and wagons by the 
excessive exertions of the team. 

FORM AND MATERIALS FOR ROADS. 

The depth of the mud in common roads is often un- 
necessarily great, in consequence of heaping together 
with the plow and scraper the soft top-soil for the raised 
carriage-way. "When heavy rains fall, this forms a 
deep bed of mud, into which the wheels work their 
way, and cause extreme labor to the team. A much 
better way is to scrape off and cart away into the fields 



FORM AND MATERIAL FOR ROADS. 



91 



adjoining all the soft, rich, upper surface, and then to 
form the harder subsoil into a slightly-rounded car- 
riage-way, with a ditch on each side. Such roads as 
this have a very hard and firm foundation, and they 
have been found not to cut up into ruts, nor to form 
much mud, even in the wettest seasons. On this hard 
foundation six inches of gravel will endure longer and 
form a better surface than twelve inches on a raised 
" turnpike" of soft soil and mud. 

It frequently happens that the form of the surface 
increases the quantity of mud in a road, by not allow- 
ing the water to flow off freely. The earth is heaped 
up in a high ridge, but having little slope on the top 
{Fig. 71), where the water lodges, and ruts are formed, 

Fig. 71. 



Badly-formed road. 

the only dry portions being on the brink of the ditches, 
where the water can escape. Instead of this form, 
there should be a gradual inclination from the centre 
to the ditches, as shown in Fig. 72. This inclination 

Fig. 72. 



Well-formed road. 

should not exceed 1 foot in 20. On hillsides the slope 
should all be toward the higher ground, as in Fig. 73. 

Fig. 73. 



. _ 




Road for side-hill. 



92 MECHANICS. 

Hard and durable roads are made on the plan of 
Telford. Their foundation is rounded stones, placed 
upright, with the smaller or sharp ends upward. The 
smaller stones are placed near the sides, and the larger 
at the centre, thus giving to the road a convex form. 
The spaces are then filled in with small broken stone, 
and the whole covered with the same material or with 
gravel. The pressure of wagons crowds it compactly 
between the stones, and forms a very hard mass. 

IMPORTANCE OF GOOD ROADS. 

The principles of road-making should be better un- 
derstood by the community at large. Farmers are 
deeply interested in good roads. Nearness to market, 
and facilities for all other kinds of communication, are 
worth a great deal, often materially affecting the price 
of land and its products. The difference between trav- 
eling ten miles through deep mud, at two miles per 
hour, with half a load, and traveling ten miles over a 
fine road, at five miles per hour, with a full load, should 
not be forgotten. 

" In the absence of such faciHties," says Gillespie, 
" the richest productions of nature waste on the spot 
of their growth. The luxuriant crops of our Western 
prairies are sometimes left to decay on the ground, be- 
cause there are no rapid and easy means of conveying 
them to market. The rich mines in the northern part 
of the State of New York are comparatively valueless, 
because the roads among the mountains are so few 
and so bad, that the expense of the transportation of 
the metal would exceed its value. So, too, in Spain 
it has been known, after a succession of abundant har- 



THE WEDGE. 93 

vests, that the wheat has actually been allowed to rot, 
because it would not repay the cost of carriage." 
Again, "When the Spanish government required a 
supply of grain to be transferred from Old Castile to 
Madrid, 30,000 horses and mules were necessary for 
the transportation of four hundred and eighty tons of 
wheat. Upon a broken-stone road of the best sort, one 
hundredth of that number could easily have done the 
work." He further adds, in speaking of the improve- 
ments in roads made by Marshal Wade in the Scottish 
Highlands, " His military road is said to have done 
more for the civilization of the Highlands than the 
preceding efforts of all the British monarchs. But the 
later roads, under the more scientific direction of Tel- 
ford, produced a change in the state of the people which 
is probably unparalleled in the history of any country 
for the same space of time. Large crops of wheat now 
cover former wastes ; farmers' houses and herds of cat- 
tle are now seen where was previously a desert ; estates 
have increased seven-fold in value and annual returns ; 
and the country has been advanced at least one hund- 
red years." 



SECTION VII. 

THE WEDGE. 



The wedge is a double inclined plane, the power 
being applied at the back to urge it forward. It be- 
comes more and more powerful as it is made more 
acute ; but, on account of the enormous amount of 
friction, its exact power can not be very accurately es- 
timated. It is nearly always urged by successive 



94 



MECHANICS. 



blows of a heavy body, the momentum of which im- 
parts to it great force. 

All cutting and piercing instruments, as knives, scis- 
sors, chisels, pins, needles, and awls, are wedges. The 
degree of acuteness must be varied according to cir- 
cumstances ; knives, for instance, which act merely by 
pressure, may be made with a much sharper angle 
than axes, which strike a severe blow. For cutting 
very hard substances, as iron, the edge must be form- 
ed with a still more obtuse angle. 

The utility of the wedge depends on the friction of 
its surfaces. In driving an iron wedge into a frozen 
or icy stick of wood, as every chopper has observed, the 
want of sufficient friction causes it immediately to re- 
coil, unless it be previously heated in the fire. The 
efficacy of nails depends entirely on the friction against 
their wedge-like faces. 



THE SCREW. 

The screw may be regarded as nothing more than 
Fig. 74. an inclined plane winding round the surface 
of a cylinder {Fig. 74). This may be easily 
understood by cutting a piece of paper in 
such a form Fig. 75. 

that its edge, 
a b (Fig. 75), 
may represent 
the inclined plane ; then, a 
beginning at the wider end, and wrapping it about the 
cylindrical piece of wood, c, the upper edg£ of the pa- 
per will represent the thread of the screw. 

Although the friction attending the use of the screw 





THE SCREW. 



95 




Screw and lever 
combined. 



is considerable, and without it it would not retain its 
place, yet the slope of its inclined thread being so grad- 
ual, it possesses great power. This power is multiplied 
to a still greater degree by the lever which is usually 
Fig 76 employed to drive it, a (Fig. 76). If, 

d for example, a screw be ten inches in 
circumference, and its threads half an 
inch apart, it exerts a force twenty 
times as great as the moving power. 
If it be moved by a lever twenty 
times as long as the diameter of the 
screw, here is another increase of 
twenty times in force. Multiplying 
20 by 20 gives 400, the whole amount gained by this 
combination, and by which a man applying one hund- 
red pounds in force could exert a pressure equal to 
twenty tons. About one third or 
one fourth of this should, how- 
ever, be deducted for friction. 

When the screw is combined 
with the wheel and axle {Fig- 
ure 77), it is capable of exert- 
ing great power, which may be 
readily calculated by multiply- 
ing the power of the screw and 

Screw, lever, and wheel ° * 

combined. fts lever into the power of the 

wheel and axle. 



Fig. 77 




96 



MECHANICS. 



CHAPTER V. 

APPLICATION OF MECHANICAL PRINCIPLES IN THE STRUC- 
TURE OF THE PARTS OF IMPLEMENTS AND MACHINES. 

In contriving the more difficult and complex ma- 
chines, the principles of mechanics must he closely 
studied, to give every part just that degree of strength 
required, and to render their operation as perfect as pos- 
sible. But in making the more common and simple 
implements of the farmer, mere guess-work too often 
hecomes the only guide. Yet it is highly useful to ap- 
ply scientific knowledge even in the shaping of a hoe- 
handle or a plow-beam. 

The simplest tool, if constantly used, should he form- 
ed with a view to the best application of strength. 
The laborer who makes with a common hoe two thou- 
sand strokes an hour, should not wield a needless 
ounce. If any part is heavier than necessary, even to 
the amount of half an ounce only, he must repeatedly 
and continually lift this half ounce, so that the whole 
strength thus spent would be equal, in a day, to twelve 
hundred and fifty pounds, which ought to be exerted 
in stirring the soil and destroying weeds. Or, take 
another instance : A farm wagon usually weighs near- 
ly half a ton ; many might be reduced fifty pounds 
in weight by proportioning every part exactly to the 
strength required. How much, then, should we gain 
here? Every farmer who drives a wagon with its 



APPLICATION OP MECHANICAL PRINCIPLES, ETC. 97 

needless fifty pounds, on an average of only five miles 
a day, draws an unnecessary weight every year equal 
to the conveyance of a heavy wagon-load to a distance 
of forty miles. 

Now a knowledge of mechanical science will often 
enable the farmer, when he selects and buys his im- 
plements, to judge correctly whether every part is prop- 
erly adapted to the required strength. We shall sup- 
pose, for instance, that he intends to purchase a com- 
mon pitchfork. He finds them differently formed, al- 
though all are made of the best materials. The han- 
dles of some are of equal size throughout. Some are 
smaller near the fork, as in Fig. 78, and others are 

Fig. 78. 
, IV 



Badly-formed fork handle. 



larger at the same place, as in Fig. 79. Now, if he 



Fig. 



Badly-formed fork handle. 

understands the principle . of the lever, he knows that 
both of these are wrongly made, for the right hand 
placed at a is the fulcrum, where the greatest strength 
is needed, and therefore the one represented by Fig. 80 



Fig 



Well-formed fork handle. 

is 'both stronger and lighter than the others. Again, 
hoe handles, not needing much strength, chiefly re- 
quire lightness and. convenience for grasping. Hence, 
in selecting from two such as are represented in the 

E 



98 MECHANICS. 

annexed figures, the one should be chosen which is 
lightest near the blade, nearly all the motion being in 
that direction, because the upper end is the centre of 
motion. The right hand, at a, acting partly as the 
fulcrum, the hoe handle should be slightly enlarged at 
that place. Fig. 81 represents a well-formed handle, 

Fig. 81. 



a 



Well-formed hoe handle. 

Fig. 82 a clumsy one. Rake handles should be made 

Fig. 82. 



U 



Badly-formed hoe handle. 

largest at the middle, or where the right hand presses. 
Rake-heads should be much larger at the centre, and 
tapering to the ends, where the stress is least, the two 
parts operating as two distinct levers, acting from the 
middle. Horse-rakes might be made considerably 
lighter than they usually are by observing the same 
principles. The greatest strength required for plow- 
beams is at the junction with the mould-board, and 
the least near the forward end, or furthest from the ful- 
crum or centre of motion. 

Now it may be that the farmer who has had much 
experience may be able to judge of all these things 
without a knowledge of the science. But this scien- 
tific knowledge would serve to strengthen his experi- 
ence, and enable him to judge more accurately and 
raiderstandingly by shn-\ying him the reasons ; and in 
many cases, where neiv implements were introduced, 
he might be enabled to form a good judgment before 



APPLICATION OF MECHANICAL PRINCIPLES, ETC. 99 



he had incurred all the expense and losses of unsuc- 
cessful trials. 

Even so simple a form as that of an ox-yoke is often 
made unnecessarily heavy. Fig. 83 represents one 

Fig. 83. 

lb/ 




that is faulty in this respect, by having been cut from 
a piece of timber as wide as the dotted lines a c, and 
being thus weakened, it requires to be correspondingly 
large. Fig. 84 is equally strong, much lighter, and is 

Fig. 84. 




easily made from a stick of timber only as wide as a b 
in the former figure. 

In the heavier machines, it is necessary to know the 
degree of taper in the different parts with accuracy. 
A thorough knowledge of science is needed to calcu- 
late this with precision, but a superficial idea may be 
given by figures. If a bar of wood, formed as in a 
(Fig. 85, p. 100), be fixed in a wall of masonry, it will 
possess as much strength to support a weight hung on 
the end as if it were the same size throughout, as b. 



100 MECHANICS. 

Fig. 85. 



^ 



.'. feiu 




^7l 



The first is equally strong with the second, and much 
lighter.* The same form doubled must be given if 
the bar is supported at the middle, with a weight at 
each end, or with the weight at the middle, supported 
at each end, as c. This form, therefore, is a proper 
one for many parts of implements, as the bars of whip- 
pie trees, the rounds of ladders, string-pieces of bridges, 
and any cross-beams for supporting weights. One 
half of this form, as a, is the proper form for rake- 
teeth, wheel-barrow handles, spade handles, &c. On 
fence-posts, the pressure being nearly alike on all parts, 
they should be nearly in the form of a wedge. There- 
fore a post of equal size throughout contains nearly 
twice as much timber as is needed for strength only. 

The form of these parts must, however, be modified 
to suit circumstances ; as whipple-trees must be large 
enough at the ends to receive the iron hooks, wagon- 

* The simple style of this work precludes an explanation of the 
mode of calculation for determining the exact form. Where the 
stick tapers only on one side, it is a common parabola; if on all 
sides, a cubic parabola. 



APPLICATION OF MECHANICAL PRINCIPLES, ETC. 101 

tongues for ironing at the end, and spade handles for 
the easy grasp of the hand. 

The axle-trees of wagons must be made not only 
strong in the middle, or at centre of pressure, but also 
at the entrance of the hub ; because the wheels, when 
thrown sideways in a rut, or on a sideling road, operate 
as levers at that point, a and b (Fig. 86), show the 
manner in which the axles of carts may be rendered 
lighter without lessening the strength, a being the 
common form, and b the improved one. 



Sometimes several forces act at once on different 
parts. For example, the spokes of wagon- wheels re- 
quire strength at the hub for stiffening the wheel ; they 
must be strong in the middle to prevent bending, and 
large enough at the outer ends, where they are soonest 
weakened by decay. Hence there should be nearly a 
uniform taper, slightly larger at the middle, and with 
an enlargement at the outer end, as c (Fig. 86). 

A very useful rule in practice, in giving strength to 
structures, is this : the strength of every square beam 
or stick to support a weight increases exactly as the 
width increases, and also exactly as the square of the 
depth increases. For example, a stick of timber eight 



102 MECHANICS. 

inches wide and four inches deep (that is, four inches 
thick), is exactly twice as strong as another only four 
inches wide, and with the same depth. It is twice as 
wide, and consequently twice as strong ; that is, its 
strength increases just as the width increases, accord- 
ing to the rule given. But where one stick of timber is 
twice as deep, the width being the same, it is four times 
stronger ; if three times as deep, it is nine times strong- 
er, and so on. Its strength increases as the square of 
the depth, as already stated. The same rule will show 
that a board an inch thick and twelve inches wide will 
be twelve times as strong when edgewise as when lying 
flat. Hence the increase in strength given to whipple- 
trees, fence-posts, joists, rafters, and string-pieces to 
farm-bridges, by making them narrow and deep. 

Again, the strength of a round stick increases as the 
cube of the diameter increases ; that is, a round piece 
of wood three inches in diameter is eight times as 
strong as one an inch and a half in diameter, and twen- 
ty-seven times as strong as one an inch in diameter. 
This rule shows that a fork handle an inch and a half 
in diameter at the middle is as much stronger than 
one an inch and a quarter in diameter, as seven is 
greater than four. Now this rule would enable the 
farmer to ascertain this without breaking half a dozen 
fork handles in trying the experiment, and it would 
enable the manufacturer to know, without the labor of 
trying many experiments, that if he makes a fork han- 
dle an inch and a half at the middle, tapering a quar- 
ter of an inch toward the ends, it will enable the work- 
man to lift with it nearly twice as much hay as with 
one an inch and a quarter only through its whole length. 



ROLLING FRICTION. 103 



CHAPTER VI. 

FRICTION. 

SECTION I. 

The subject of friction has been postponed, or has 
been merely alluded to, in treating heretofore of ma- 
chines, to prevent the confusion of considering too many 
things at once. As it has often an important influence 
on the action of machines, it is worthy of careful in- 
vestigation. 

It is familiar to most persons, that when two sur- 
faces slide over each other while pressing together, the 
minute unevenness or roughness of their surfaces causes 
some obstruction, and more or less force is required. 
This resistance is known as friction. 

ROLLING FRICTION. 

The term is also applied to the resistance of one body 
rolling over another. This may be observed in various 
degrees by rolling an ivory ball successively over a car- 
pet, a smooth floor, and a sheet of ice ; the same force 
which would impel it only a few feet on the carpet, 
would cause it to move as many yards on a bare floor, 
and a still greater distance on the ice. The two ex- 
tremes may be seen by the force required to draw a 
carriage on a deep sandy or loose-gravel road, and on 
a rail-road. 



104 MECHANICS. 

NATURE OF FRICTION. 

If two stiff bristle brushes be pressed with their faces 
together, they become mutually interlocked, so that it 
will be quite difficult to give them a sliding motion. 
This may be considered as an extreme case of friction, 
and serves to show its nature. In two pieces of coarse, 
rough sandstone, or of roughly-sawed wood, asperities 
interlock in the same way, but less in degree ; a di- 
minished force is consequently required in moving the 
two surfaces against each other. On smoothly-planed 
wood the friction is still less ; and on polished glass, 
where the unevenness can not be detected without the 
aid of a powerful magnifying glass, it is reduced still 
further in degree. 

ESTIMATING THE AMOUNT OF FRICTION. 

In order to determine the exact amount of friction 
between different substances, the following simple and 
ingenious contrivance is adopted : an inclined plane, 
a b (Fig: 87), is so formed that it may be raised to any 

Fig. 87. 




desired height by means of the arc of a circle and a 
screw. Lay a flat surface of the substance we wish 
to examine upon this inclined plane, and another small- 



ESTIMATING THE AMOUNT OP FRICTION. 105 

er piece or block of the same substance upon this 
surface; then raise the plane until it becomes just 
steep enough for the block to slide down by its weight. 
Now, by measuring the degree of slope, we know at 
once the amount of friction. Suppose, for example, the 
two surfaces be smoothly-planed wood : it will be found 
that the plane must be elevated about half as high as 
its length ; therefore we know, by the properties of the 
inclined plane, heretofore explained, that it requires a 
force equal to one half the weight of the wooden block 
to slide it over a smooth wooden surface. Some kinds 
of wood have more friction than others, but this is about 
the average. 

From the result of this experiment we may learn 
that to slide any object of wood across a floor requires 
an amount of strength equal to one half the weight of 
the object. A heavy box, for instance, weighing two 
hundred pounds, can not be moved without a force 
equal to one hundred pounds. It also shows the im- 
propriety of placing a heavy load upon a sled in winter 
for crossing a bare wooden bridge or a dry barn floor, 
the friction between cast-iron sleigh-shoes and rough 
sanded plank being nearly equal to one third of the 
whole weight* Hence a load of one ton (including 
the sled) would require a draught equal to more than 
six hundred pounds, which is too much for an ordina- 
ry single team. On bare unfrozen ground the friction 
would be still greater. On a plank bridge, with run- 
ners wholly of wood, it would be equal to half the load. 
All these facts may be readily proved by actually 

* On clean hard wood, -with polished metallic shoes, the friction 
would be much less, or a fourth, or fifth. 



106 MECHANICS. 

placing the sled on slopes of plank and of earth, and 
by observing the degree of steepness required for slid- 
ing down by its own weight. 

In a similar way, we are enabled easily to ascertain 
the force required to draw a wagon upon any kind of 
level surface. Suppose, for example, that we wish to 
determine the precise amount of force for a wagon 
weighing, with its load, one ton, on a plank road. Se- 
lect some slight descent, where the wagon will barely 
run with its own weight. Ascertain by a level just 
what the degree of descent is ; then divide the weight 
of the wagon by the degree of the slope, and we shall 
have the force sought for. To make this rule plainer 
by an example : it will be found that a good, newly- 
laid plank track, if it possess a descent of only one foot 
in fifty feet distance, will be sufficient to give motion 
to an easy-running wagon ; therefore we know that 
the strength required to draw it on a level will be only 
one fiftieth part of a ton, or forty pounds. 

The resistance offered to the motion of a wagon by 
a Macadam road, by a common dry road, and by one 
with six inches of mud, may be readily determined in 
the same way by selecting proper slopes for the exper- 
iment. If by such trials as these the farmer ascer- 
tains the fact that a few inches of mud are sufficient 
to retard his wagon so much that it will not run of its 
own weight down a slope of one foot in four (and few 
common roads are ever steeper), then he may know 
that a force equal to one fourth the whole weight of 
his wagon and load will be required to draw it on a 
level over a similar road — that is, the enormous force 
of five hundred pounds will be needed for one ton, of 



RESULTS WITH THE DYNAMOMETER. 107 

which many wagons will constitute nearly one half. 
Hence he can not fail to see the great importance, for 
the sake of economy, and humanity to his team, of pro- 
viding roads, whether public or private, of the hardest 
and best materials. 



SECTION II. 

RESULTS WITH THE DYNAMOMETER. 

Another mode of determining the resistance of roads 
is by means of the Dynamometer.* It resembles a 
spring-balance, and one end is fastened to the wagon 
and the other end connected with the horses. The 
force applied is measured on a graduated scale, in the 
same way that the weight of any substance is meas- 
ured with the spring-balance. A more particular 
description of this instrument will be given hereafter. 

Careful experiments have been made with the dyna- 
mometer to ascertain accurately the resistance of va- 
rious kinds of roads. The following are some of the 
results : 

On a new gravel road, a horse will draw eight times 
as much as the force applied ; that is, if he exerts a 
force equal to one hundred and twenty-five pounds, he 
will draw half a ton on such a road, including the 
weight of the wagon, the road being perfectly level. 

On a common road of sand and gravel, sixteen times 
as much, or one ton. 

On the best hard-earth road, twenty-five times as 
much, or one and a half tons. 

On a common broken-stone road, twenty-five to thir- 

* From two Greek -words, dunamis, power, and metreo, to measure. 



108 



MECHANICS. 



ty-six times as much, or one and a half to two and a 
quarter tons. 

On the best broken-stone road, fifty to sixty-seven 
times as much, or three to four tons. 

On a common plank-road, clean, fifty times as much, 
or three tons. 

On a common plank-road, covered thinly with sand 
or earth, thirty to thirty-five times as much, or about 
two tons. 

On the smoothest oak plank-road, seventy to one 
hundred times as much, or four and a half to six tons. 

On a highly-finished stone track-way, one hundred 
and seventy times as much, or ten and a half tons. 

On the best rail-road, two hundred and eighty times 
as much, or seventeen and a half tons. 

The firmness of surface given to a broken-stone road 
by a paved foundation was found to lessen the resist- 
ance about one third. 

On a broken-stone road it was found that a horse 
could draw only about two thirds as much when it was 
moist or dusty as when dry and smooth ; and when 
muddy, not one half as much. When the mud was 
thick, only about one quarter as much. 

The character of the vehicle has an influence on the 
draught. Thus, a cart, a part of the load of which is 
supported by the horse, usually requires only about 
two thirds the force of horizontal draught needed for 
wagons and carriages. On rough roads the resistance 
is slightly diminished by springs. 

On soft roads, as earth, sand, or gravel, the number 
of pounds draught is but little affected by the speed ; 
that is, the resistance is no greater in driving on a trot 



WIDTH OP WHEELS. 109 

than on a walk ; "but on hard roads it becomes greater 
as the velocity increases. Thus a carriage on a dry 
pavement requires one half greater force when the 
horses are on a trot than on a walk ; but on a muddy 
road the difference between the two rates of speed is 
only about one sixth. On a rail-road, where a draught 
of ten pounds will draw a ton ten miles an hour, the 
resistance increases so much at a high degree of speed 
as to require a force of fifty pounds per ton at sixty 
miles an hour — that is, it would require five times as 
much actual power to draw a train one hundred miles 
at the latter rate as at the former ; but as the speed 
is six times as great, the actual force during a given 
time would be five times six, or thirty times as great. 

WIDTH OF WHEELS. 

Wheels with wide tire run more easily than narrow 
tire, on soft roads ; on hard, smooth roads, there is no 
sensible difference. "Wide tire is most advantageous 
on gravel and new broken-stone roads, both by causing 
the vehicles to run more easily, and by improving the 
surface. For the latter reason, the New York turnpike 
law allows six-inch wheels to pass at half price, and 
twelve-inch wheels to pass free of toll. Wheels with 
broad tire on a farm would pass over clods, and not 
sink between them; or would only press the surface 
of new meadows, without cutting the turf. But where 
the ground becomes muddy, the mud closes on both 
sides of the rim, and loads the wheels. On clayey 
soils, narrow tire unfits the roads for broad wheels. 
For these reasons, broad wheels are decidedly objection- 
able for clayey or soft soils, and they are chiefly to be 



110 MECHANICS. 

recommended for broken-stone roads, and gravelly, or 
dry, sandy localities. They are also much the best for 
the wheels of sowing or drilling machines, which only 
pass over mellowed surfaces. 

The larger the wheels are made, the more easily they 
run ; thus a wheel six feet in diameter meets with only 
half the resistance of a wheel three feet in diameter. 

A flat piece of wood, sliding on one of its broad sur- 
faces, is subject to the same amount of friction as when 
sliding upon its edge. Hence the friction is the same, 
provided the pressure be the same, whether the surface 
be small or large.* Or, in other words, if the surfaces 
are the same, a double pressure produces a double 
amount of friction ; a triple pressure, a triple amount, 
and so on. 

A narrow sleigh-shoe usually runs with least force, 
for two reasons : first, its forward part cuts with less re- 
sistance through the snow ; and, secondly, less force is 
required to pack the narrow track of snow beneath it. 
The only instance in which a wide sleigh-shoe would be 
best, is where a crust exists that would bear it up, and 
through which a narrow one would cut and sink down. 

VELOCITY. 

Friction is entirely independent of velocity ; that is, 
if a force of ten pounds is required to turn a carriage 
wheel, this force will be ten pounds, whether the car- 
riage is driven one or five miles per hour. Of course, 
it will require five times as much force to draw five 

* Generally speaking, this is very nearly correct ; but when the 
pressure is intense, the friction is slightly less on the smaller sur- 
face. 



FRICTION AT THE AXLE. 



Ill 



miles per hour, because five times the distance is gone 
over ; but, measured by a dynamometer or spring-bal- 
ance, the pressure would be the same. In precisely 
the same way, the weight of a stone remains the same, 
whether lifted slowly or quickly by a lever. If the 
friction of the wheels of a wagon on their axles be 
equal to ten pounds, driving the horse fast or slowly 
will not increase or diminish it. But fast driving will 
require more strength, for the same reason that a man 
would need more strength to carry a bag of wheat up 
two flights of stairs than one, in one minute of time. 



FRICTION AT THE AXLE. 

A carriage wheel, or any other wheel revolving on an 
axle, will run more easily as the axle is made smaller. 
This is not owing to the rubbing surfaces being less in 
size, as some mistakenly suppose, for it has just been 
shown that this makes very little or no difference, pro- 
vided the pressure is the same ; but it is owing to the 

leverage of the wheel 
on the friction at the 
axis ; and the smaller 
the axle, the greater 
is this leverage ; for, 
if the axle, a {Fig- 
ure 88), be six inches 
in circumference, and 
the wheel, b c, be ten 
feet in circumference, 
then the outer part of 
the wheel will move 
twenty times further than the part next the axle. 




112 MECHANICS. 

Therefore, according to the rule of virtual velocities, 
one ounce of force at the rim of the wheel will over- 
come twenty ounces of friction at the axle ; or if the 
axle were twice as large, then, according to the same 
rule, it would require two ounces to overcome the same 
friction acting between larger surfaces. 

For this reason, large wheels in wheel- work for mul- 
tiplying motion, if not made too heavy, run with less 
force than smaller ones, the power acting upon a larger 
lever. Horse-powers for thrashing-machines, consist- 
ing chiefly of a large, light crown-wheel, well stiffened 
by brace-work, have been found to run with remarka- 
ble ease ; a good example of which exists in what is 
known as Talpiri's horse-power, when made in the 
best manner. 

FRICTION-WHEELS. 

On the preceding principle, friction-wheels or fric- 
tion-rollers are constructed, for lessening as much as 
Fig. 89. possible the friction of axles in certain 

cases. By this contrivance, the axle, a 
{Fig. 89), instead of revolving in a sim- 
ple hole or cavity, rests on or between 

FrictUm-wheels. ^ edgeg of ^ other wheds Ag ^ 

axle revolves, the edges turn with it, and the rubbing 
of surfaces is only at the axles of these two wheels. 
If, therefore, these axles be twenty times smaller than 
the wheels, the friction will be only one twentieth the 
amount without them. This contrivance has been 
strongly recommended and considerably used for the 
cranks of grindstones (Fig. 90), but it was not found 
to answer the intended purpose so well as was expect- 




■■<^. 



LUBRICATING SUBSTANCES. 



113 



Fig. 90. 




IhM 


(Ifpl^^^ 


p? 1 


Willi' 1 ' 1 


°?T\ '■■■'• 


IIIIp'P 



ZTZ ~ ^~- ^---Y^ 



not, 



llilll 

Grindstone on Friction-wheels. 

of course, remove. 



ed, for the very- 
plain reason that, 
in using a grind- 
stone, nearly all 
the friction is 
at the circumfer- 
ence, or between 
the stone and the 
tool, which fric- 
tion-wheels could 



SECTION III. 



LUBRICATING SUBSTANCES. 



Lubricating substances, as oil, lard, and tallow, ap- 
plied to rubbing surfaces, greatly lessen the amount of 
friction, partly by filling the minute cavities, and partly 
by separating the surfaces. In ordinary cases, or where 
the machinery is simple, those substances are best for 
this purpose which keep their places best. Finely- 
powdered black-lead, mixed with lard, is for this reason 
better for greasing carriage wheels than some other ap- 
plications. Drying oils, as linseed, soon become stiff 
by drying, and are of little service. Olive oil, on the 
contrary, and some animal oils, which scarcely dry at 
all, are generally preferred. To obtain the full benefit 
of oil, the application must be frequent. 

According to the experiments made with great care 
by Morin, at Paris, the friction of wooden surfaces on 
wooden surfaces is from one quarter to one half the 
force applied ; and the friction of metals on metals, one 



114 MECHANICS. 

fifth to one seventh' — varying in both cases with the 
kinds used. "Wood on wood was diminished by lard 
to about one fifth to one seventh of what it was before ; 
and the friction of metal on metal was diminished to 
about half what it was before ; that is, the friction be- 
came about the same in both cases after the lard was 
applied. 

To lessen the friction of wooden surfaces, lard is bet- 
ter than tallow by about one eighth or one seventh ; 
and tallow is better than dry soap about as two is to 
one. For iron on wood, tallow is better than dry soap 
about as five is to two. For cast iron on cast iron, 
polished, the friction with the different lubricating sub- 
stances is as follows : 

Water 31 

Soap ?0 

Tallow 10 

Lard *T 

Olive oil 6 

Lard and black-lead 5 

When bronze rubs on wrought iron, the friction with 
lard and. black-lead is rather more than with tallow, 
and about one fifth more than with olive oil. With 
steel on bronze, the friction with tallow and with olive 
oil is about one seventh less than with lard and black- 
lead. 

As a general rule, there is least friction with lard 
when hard wood rubs on hard wood ; with oil, when 
metal rubs on wood, or metal on metal — being about 
the same in each of all these instances. 

In simple cases, as with carts and wagons, where 
the friction at the axle is but a small portion of the re- 



ADVANTAGES OF FRICTION. 115 

sistance,* a slight variation in the effects in the lubri- 
cating substance is of less importance than retaining 
its place. In more complex machinery, as horse-pow- 
ers for thrashing-machines, friction becomes a very- 
large item, unless the parts are kept well lubricated 
with the best materials. 

Leather and hemp bands, when used on drums for 
wheel- work, should possess as much friction as possi- 
ble, to prevent slipping, thus avoiding the necessity of 
tightening them so much as to increase the friction of 
the axles. "Wood with a rough surface has one half 
more friction than when worn smooth ; hence moisten- 
ing and rasping small drums may be useful. Facing 
with buff leather or with coarse thick cloth also ac- 
complishes a useful purpose. It often happens that 
wetting or oiling bands will prevent slipping, by keep- 
ing their surfaces soft, and causing them to fit more 
closely the rough surface of the drum. 

ADVANTAGES OF FRICTION. 

Although friction is often a serious inconvenience, or 
loss, in lessening the force, of machines, there are many 
instances in which it performs important offices in na- 
ture and in works of art. " Were there no friction, all 
bodies on the surface of the earth would be clashing 
against each other ; rivers would dash with an un- 
bounded velocity, and we should see little besides col- 

* If the friction at the axle be one twelfth of the force, and the 
diameter of the wheels ten times as great as the diameter of the axle, 
the friction at the axles will be reduced to one twelfth of a tenth, or 
one hundred and twentieth part of the force, according to the law 
of virtual velocities as applied to the wheel and axle. 



116 MECHANICS. 

lision and motion. At present, whenever a body ac- 
quires a great velocity, it soon loses it by friction 
against the surface of the earth. The friction of water 
against the surfaces it runs over soon reduces the rap- 
id torrent to a gentle stream ; the fury of the tempest 
is lessened by the friction of the air on the face of the 
earth, and the violence of the ocean is subdued by the 
attrition of its own waters. 

" Its offices in the works of art are equally import- 
ant. Our garments owe their strength to friction, and 
the strength of ropes depends on the same cause ; for 
they are made of short fibres pressed together by twist- 
ing, causing a sufficient degree of friction to prevent 
the sliding of the fibres. Without friction, the short 
fibres of cotton could never have been made into such 
an infinite variety of forms as they have received from 
the hands of ingenious workmen."* Deprived of this 
retaining force, the parts of stone walls, piles of wood 
and lumber, and the loads of carts and wagons, as well 
as the wheels themselves, would slide without restraint, 
as if their surfaces were of the most icy smoothness, 
and walking without support would be impossible. 

The tractive power of locomotives depends on the 
friction between the wheels and iron rails, which is 
equal to about one fifth of the weight of the engine ; 
that is, a locomotive weighing twenty-five tons will 
draw with a force of five tons, without producing slip- 
ping of the wheels. 

* Encyclopaedia Americana. 



PRINCIPLES OF DRAUGHT. 117 



SECTION - IV. 

PRINCIPLES OF DRAUGHT. 

An examination of the nature or laws of friction en- 
ables us to ascertain the best line of draught for teams 
when attached to wagons and carriages. If there were 
no friction whatever upon the road, the best direction 
for the traces would be parallel to the road, that is, on a 
level with the wagon ; but as there is always some fric- 
tion, the line of draught should be a little rising, so as 
to tend to lessen the pressure of the wheels on the road. 
Now this upward direction of the draught should al- 
ways be exactly of such a slope, that if the same slope 
were given to the road, the wagon would just descend 
by its weight. The more rough or muddy the road is, 
the steeper should be this line of draught or direction 
of the traces.* On a good common road it would be 
much less, and on a plank road but slightly varied 
from a horizontal direction. On a rail-road the line 
should be about level. On good sleighing, some of the 
strength of the team is commonly lost by too steep a 
line of draught. 

The reason of this rule may be understood by the 
Fig. 91. following explanation: Let the ob- 

struction, a, in the annexed figure 
(Fig. 91), represent the friction the 
wheel constantly meets with in roll- 
ing over a common road. To over- 
come this Motion, the wheel must 

* Provided the wheels are not made smaller for this purpose, in- 
creasing their resistance. 




118 



MECHANICS. 



rise in the direction of the dotted line. Therefore, if 
the force is made to pull in this direction, it will act 
more advantageously than in any other, because this 
is the course in which the centre of the wheel must 
move. Now if a downward slope were given to the 
road at this obstruction, the wheel and the obstruction 
would be brought both on a level, and the wheel would 
move with the slightest degree of force. 

It will be understood from the preceding rule that a 
sled running on bare ground should be drawn by traces 
bearing upward in a large degree. The same remark 
will apply to the plow, which slides upon the ground 
in a similar way, with the pressure of the turning sod 
as a load. Hence the reason that a great saving of 
strength results from the use of short traces in plowing. 
An experiment was tried for the purpose of testing this 
reasoning ; first, with traces of such length that the 
horses' shoulders were about ten feet from the point of 
the plow ; and secondly, with the distance increased to 
about fifteen feet. With the, short traces a strength 
was required equal to 2£ cwt., but with the long traces 
it amounted to 3 J cwt. 

But the draught-traces may be made too short. 
When this is the case, the plow is necessarily thrown 
too much upon its point to keep it from flying out of 
the ground, by which means it works badly in turning 
the furrow. In addition to this evil, the plowman is 
compelled to bear down heavily, adding to the friction 
of the sole on the bottom of the furrow, and greatly in- 
creasing his labor. 

The line of draught should be so adjustsd that the 
plow may press equally all along on its sole or bottom, 



PRINCIPLES OF DRAUGHT. 



119 



which will cause it to run evenly and with a steady mo- 
tion. This end will be effected by giving the traces or 
draught-chain just such a length that the share of the 
plow (or centre of resistance), the clevis, and the point 
of draught at the horses' shoulders (or the ring of the 
ox-yoke) shall all form a straight line. This is shown 
in the annexed figure, where A is the place of the ox- 
ring or of the for- 
a^-- ward extremity of 
-'•'' the traces {Figure 

! 92). 
L — r^Q centre of re- 



Fig. 92. 




sistance will vary with the depth of plowing. When 
the furrow is shallow (as shown by the lines G- H, Fig. 
93), the centre of resistance will be at A, requiring the 

Fig. 93. 




Line of draught for the plow. 

team to be fastened to the lower side of the clevis, C ; 
but when the depth is greater (as shown by F H), the 
centre of resistance will be at B, requiring a higher at- 
tachment to the clevis; the point of draught, E, re- 
maining the same in both cases. 

So great is the difference between an awkward and 
skillful adjustment of the draught to the plow, that 
some workmen with a poor instrument have succeeded 
better than others with the best ; and plows of second 
quality have sometimes, for this reason, been preferred 
to those of the most perfect construction. 



120 MECHANICS. 

COMBINED DRAUGHT OF ANIMALS. 

When several animals are combined together, it is 
of great importance that they should be exactly match- 
ed in gait. Much force is often wasted when they 
draw unsteadily or unevenly. It is more difficult to 
divide the draught equally among several animals when 
placed one before the other, or ad tandem, than when 
arrayed abreast, for some may hang back, and others 
do more than their share, unless a skillful driver is 
always on the watch. It also happens, when thus 
arranged, that the forward horses draw horizontally, 
while the hindmost one draws in a sloping line, and 
the line of draught between them thus being crooked, 
more or less force is lost. This may be, however, rem- 
edied in part by placing the taller animals forward, and 
the smaller behind. 

For these reasons, when only three horses are used, 
they should always be placed abreast. The force re- 
quired for each may be rendered exactly equal by the 
whipple-trees usually employed for this purpose, and 
represented in Fig. 94, where two horses are attached 

Fig. 94. 




Whipple-treefor three horses. 

\o the shorter end, and the third to the longer end of 
the common bar. Another ingenious but more com- 
plex arrangement is shown by Fig. 95, where also the 
central horse has only half the two others, by being 



PRINCIPLES OF DRAUGHT. 
Fig. 95. 



121 




Whipple-tree for three horses. 

attached to the longer ends of the intermediate bars. 
Fig. 96 represents the mode of attaching four horses in 
draught, their force being equalized by passing the 

Fig. 96. 




Whipple-tree for four horses. 

chain round the wheel in the pulley-block, a, security 
being provided that the hindmost pair shall not en- 
croach on the forward pair, by connecting the end of 
the chain at the same time to the plow. 

F 



122 MECHANICS. 

SECTION V. 

CONSTRUCTION AND USE OF THE DYNAMOMETER. 

The dynamometer, or force-measurer, has been al- 
ready briefly alluded to, but a more particular descrip- 
tion will be useful. In the construction and selection 
of all machines and implements that require much 
power in their use, the dynamometer is indispensable, 
although at present but little known. As an example 
of its utility, the farmer may wish to choose between 
two plows which, so far as he can perceive, may do 
their work equally well ; but this instrument, when 
applied, may show that the team must draw with a 
force equal to 400 pounds in moving one of them 
through the soil, while 300 pounds would be sufficient 
for the other. He would, therefore, select the one of 
easiest draught, and by doing so would save the labor 
of one day in four to his team, or twenty-five days in 
a hundred, which would be worth many times the cost 
of the trial. The same advantage might be derived 
in the selection of harrows, cultivators, horse-rakes, 
straw-cutters, and all other implements drawn by 
horses or worked by men. Again, the farmer may be 
in doubt in choosing between two thrashing-machines, 
which in other respects may work equally fast and 
well ; but the dynamometer may show that one re- 
quires a severer exertion from the team, and conse- 
quently is less valuable for use. 

The operation of this instrument may be readily un- 
derstood by Figure 97, where b represents the dyna- 
mometer, made precisely similar to a large and stiff 



CONSTRUCTION AND USE OF THE DYNAMOMETER. 123 




Dynamometer, or Force-measurer. 



spring balance, with one hook attached to the plow 
and the other to the whipple-tree. The amount of 
force required to draw the plow is accurately meas- 
ured on the scale by the index or pointer, a. 

Sometimes the motion of this index is multiplied, or 
made greater and more easily seen, by means of a cog- 
wheel and rack- work ; but this renders the instrument, 
at the same time, more complex. 

Another form of this instrument is shown in Fig. 98, 




Elliptic Dynamometer. 

where the ends of the oval spring, Q, Q,, are attached 
to the plow and draught. The harder the force exert- 
ed by the team, the closer together will the sides of 
this spring be brought, causing the rod, E, to press 
against the index or pointer, and showing the precise 
degree of force on the circular scale. 



124 



MECHANICS. 



An improvement, by rendering the instrument more 
compact, is shown in Fig. 99, where S S is the spring, 
and directly over it is the graduated scale. 



Fig. 99. 




Elliptic Dynamometer, in compact form : S S, spring ; F, cross-lever for moving 

index. 

An inconvenience occurs in the use of the instru- 
ments now described from the rapid vibration of the 
index, resulting from the quick changes in the force, 
partly from inequalities in the soil, and partly from the 
unsteady motion of the horses. The vibration is some- 
times so great that the index can be hardly seen, ren- 
dering it difficult to measure the average force. This 
inconvenience has been removed, in a great degree, by 
attaching to one end of the index, E (Fig. 99), a pis- 
ton working in a cylinder filled with oil, C ; this piston 
has a small hole through it, through which the oil pass- 



SELF-RECORDING DYNAMOMETER. 



125 



es from one side to the other as the draught varies, but 
not fast enough to allow any sudden motion. 

SELF-RECORDING DYNAMOMETER. 

A less simple but more perfect instrument is the Self- 
recording Dynamometer, which marks accurately all 
the vibrations on a slip of paper while the plow is in 
operation. A pencil is fixed to the index, and presses, 
by means of a spring, against the paper, thus giving a 
true register of the force exerted. To prevent the pen- 
cil from constantly marking on the same line, the pa- 
per is made to move slowly in a side direction, so that 
all the vibrations are shown, as represented in Fig. 100, 

Fig. 100. 



-*% — -JfiSis Motiojz- ef/?a/?cr „ n 


300 


i ayv 

1 t> sun 




ll 


| 


li ll 


260 








i 


\ 240 




a 




I 




HI 1 


ft 220 


,1 


I 


I, ii 




1 1 


la ' 


'I'll 


200 




ill! 


lillr 


\ 






180 




Ill 




I 1 ,! 








160 






I 1 


1- " 






440 




1 






120 










100 










80 










60 










40 










20 













The markings of the Self-recording Dynamometer. 

and they may be accurately examined and read off at 
leisure, a and b representing the forces of two different 
plows, drawn through a single furrow across the field. 
The motion of the paper is effected by being placed on 
two rollers, one of which unwinds it from the other. 




126 MECHANICS. 

This roller is made to turn by means of a wheel run- 
ning on the ground, which gives motion to the roller 
through an endless chain, working a cog-wheel hy 
means of an endless screw. The cylindrical dynamom- 
eter, shown in Fig. 101, is used for this purnose, length- 
Fig. 101.^ wise upon which the two 
rollers are placed for hold- 
ing the paper. "With this in- 
strument a permanent reg- 
ister might he made of the 
Seif-recorking Dynamometer. force required for different 
plows, the accuracy of which none could dispute. 

DYNAMOMETER FOR ROTARY MOTION. 

All these dynamometers apply only to simple, on- 
ward draught, as in plowing, drawing wagons, harrow- 
ing, &c. There is another, represented in Fig. 102, of 
very ingenious hut complex construction, which shows 
the force required in working any rotary machine, such 
as thrashers, straw-cutters, and mills, and showing, at 
the same time, the velocity, and recording the numher 
of revolutions made. 

The whole machine is supported by a cast-iron frame- 
work, on four small wheels with flanges, like the 
wheels of rail-cars, that it may he conveniently run up 
on a temporary rail- way to the thrashing or other ma- 
chine to he tried. 

The band- wheel, /, on the shaft, e, is connected with 
the machine under trial, and the force is supposed, in 
this instance, to be applied by hand to the handle, a, 
on the fly-wheel. 

When the fly-wheel is turned in the direction shown 



DYNAMOMETER FOR ROTARY MOTION. 



127 



by the arrow, it causes the two cog-wheels to revolve, 
Fig. 102. 




Dynamometer for measuring the force and velocity of thrashing-machines. 

and moves the hand in the direction shown by the oth- 
er arrow. Now, whatever force is required to turn the 
wheel, /, connected with the machine under trial, must 
be overcome by a corresponding force applied to the 
handle, a, because the wheel- work is so adjusted that 
this handle moves with the same velocity as the band 
on the band- wheels. 

The wheel, /, being connected by the band to the 
wheel, d, which is on the same axis or shaft as the cog- 
wheel, /, the resistance of the machine under trial tends 
to keep the cog-wheel, /, from turning, until enough 
force is applied to the handle, a, to set the cog-wheel, 
k, in motion. Now the greater the resistance, the 
greater will be the power needed at the handle. This 



128 MECHANICS. 

power, therefore, is measured accurately in the follow- 
ing manner : 

The axle, g, of the cog-wheel, I, rests at its further 
end in an oolong hole or mortise, that allows it liberty 
to play, or rattle up and down within narrow limits. 
This same axle, g, passes through a hole in the lever, 
i, so that when it rattles up and down, it carries this 
lever up and down with it. The other part of the lev- 
er turns on the shaft, h, of the other cog-wheel. 

Now when the man at the fly-wheel applies his 
force to the handle, a, the resistance of the machine 
under trial causes the cog-wheel, /, to refuse to turn ; 
consequently, his force, instead of turning it, lifts it up 
in the mortise, and raises the lever with it. As he in- 
creases his force against the handle, let weights he 
hung on the lever, until, at the very moment that the 
wheel begins to revolve, the weights shall be just heavy 
enough to keep the lever down in the mortise. This 
weight, therefore, will measure the exact force need- 
ed to turn the machine : the greater the resistance of 
the machine, the greater must be the weight. 

There is another weight, /, used to balance the 
lever and cog-wheel, I, while the machine is at rest, or 
before the force is applied to it, so that the weight at 
m shall represent the force truly. The weight, m, is, 
of course, to be multiplied by the power it exerts on 
the lever, i, which should be graduated like the bar of 
a steelyard. 

There are a few other parts of this dynamometer not 
yet described. One is the cylinder, o, filled with oil, 
in which a perforated piston works, preventing the 
rapid vibration of the lever, i, as the force varies, pre- 



DYNAMOMETER FOR ROTARY MOTION. 129 

cisely similar to the cylinder of oil described in Fig. 
99. Another part is the pendulum, p, with the wheel, 
r, which measures the time. 

The use of this instrument has been already attend- 
ed with some important results in detecting the great 
amount of friction existing in some thrashing-machines 
of high reputation, which has been found to amount, 
in certain cases, to more than one half of the whole 
power applied. It is only by detecting so great a 
waste that we are enabled to take measures for its 
prevention. 

F2 



130 MECHANICS. 



CHAPTER VII. 

CONSTRUCTION AND USE OF FARM IMPLEMENTS AND MA- 
CHINES. 

SECTION I. 

The application of mechanical principles in the 
structure of the simpler parts of implements and ma- 
chines has been treated of in a former part of this 
work. It remains to examine more particularly those 
machines chiefly important to the farmer, and to show 
the application of these principles in their use and op- 
eration. 

PLOWS AND PLOWING. 

One great difference between good and had plows is 
in the form of the mould-hoard. To understand the 
best form, it must be observed that the slice is first cut 
by the forward edge, and then one side is gradually 
raised until it is turned completely over, or bottom side 
up. To do this, the mould-board must combine the 
two properties of the wedge and the screw. 

The position of the furrow-slice, from the time it is 
first cut till completely inverted, may be represented 
by placing a leather strap fiat upon a table, and then, 
while holding one end, turning over the other, so as 
to bring that also fiat upon the table, as in Fig. 103. 
Now the mould-board should have just such a shape 
as will fit the furrow-slice while in the act of turning 



PLOWS AND PLOWING. 



131 



over, else it will wear unequally, become clogged with 
soil where the earth rubs slightly, and require greater 
strength in the team. By examining, it will he found 
that, although the strap (Fig. 103) twists like a screw, 

Fig. 103. 



yet all parts will be straight if measured across at right 
angles, as shown by the dotted lines. Therefore, by 
applying this principle, the farmer can judge of one im- 
portant quality in selecting a plow. If, for example, 
he finds that a straight-edged stick will be flat upon 
Fig- 104. the face at right angles to the 

line of motion, as shown by the 
dotted lines in Fig. 104, the 
mould-board will be so far 
right; but if the straight edge 
must be placed in other posi- 
tions, as in Fig. 105, it is de- 
fective in form. A mould- 
board may be much modified, 
with this principle preserved in every instance ; that is, 
it may be short, so as to raise the earth abruptly, or it 
may be long, so as to raise it gradually ; it may be 
adapted to a deep furrow, lifting the furrow-slice to a 
considerable height, or to a shallow one, throwing it 
quickly over. These modifications are required for dif- 
ferent soils and for different purposes. "When, for ex- 
ample, it is desired to break up the slice and pulverize 
a heavy soil, the twist must be short and abrupt ; when 
a sod in light soil is to be inverted smoothly, the mould- 
board must be longer, and the twist more gradual. In 





132 MECHANICS. 

all mould-boards, care must be taken that the soil is 
not lifted so abruptly as to throw it forward, instead of 
simply turning it over. 

Another defect in some plows is too blunt or thick a 
Fig. 106. wedge formed by the share and mould- 

board. By the plow represented in 
Fig. 106, the earth must be thrown 
from the land-side into the furrow 
with a velocity about equal to the 
motion of the team; but by the 
one shown by Fig. 107, the team 
moves twice as fast as the earth is 
thrown by this longer wedge. C on- 
sequently, according to the rule of virtual velocities 
(already explained), as applied to the wedge, there is 
a great gain in power. Care must be taken, how- 
ever, not to make this wedge too long, else the friction 
of a greater length of sod may overbalance the advant- 
age. 

An attention to such principles as these has result- 
ed in an extraordinary improvement within the past 
thirty years. Plows are made with one third the for- 
mer cost, that will do more than twice as much work 
with the same strength of team, and do it so much 
better, that larger crops may be reaped from the same 
land. These advantages are so great, that on all the 
arable land of the Union there must be a yearly sav- 
ing of ten millions of dollars in the work of teams, one 
million in the price of plows, and millions of bushels 
in the aggregate increase of crops by good tillage. In 
the two annexed figures we have a representation of 
an old and an improved plow. 



PLOWS AND PLOWING. 133 

Fig. 108 is such a plow as is now used in some 




parts of Germany. Fig. 109 is one of the best im- 




proved cast plows. Nearly as great a difference ex- 
ists between the plows used here fifty years ago and 
at the present time. Some portion of this great im- 
provement may have been effected by persons not fa- 
miliar with science ; but if such persons were enabled 
to achieve so much, with the few truths which they 
had themselves laboriously discovered, how much more 
they might have accomplished if they had enjoyed the 
advantages of all that strong-minded men have discov- 
ered during the course of ages, and which is collected 
together in the form of modern science. How much 
more, too, would be saved in time and tedious exper- 
iments, by applying the principles of science already 



134 MECHANICS. 

discovered, than by ascertaining what we wish to know 
only by long-repeated trials. 

TRENCH AND SUBSOIL PLOWING. 

When the common two-horse plow alone is used by 
farmers, it pulverizes the soil only a few inches in 
depth, and its own weight, and the tread of the horses 
on the bottom of the furrow, gradually form a hard 
crust at that depth, through which the roots of plants 
and the moisture of rains do not easily penetrate. 
Hence the roots have only a few inches of good soil on 
the surface of the earth for their support and nourish- 
ment ; and when heavy rains fall, the shallow bed of 
mellow earth is soaked and injured by surplus water. 
Again, in time of drought, this shallow bed of moist- 
ure is soon evaporated, and the plants suffer in conse- 
quence. 

But, on the other hand, when the soil is made deep, 
it absorbs, like a sponge, all the rains that fall, and 
gradually gives off the moisture as it is wanted dur- 
ing hot and dry seasons. For this reason, deep soils 
are not so easily injured by excessive wetness, or by ex- 
treme drought, as shallow ones. In addition to this 
advantage, they allow a deeper range for the roots in 
search of nourishment. 

Soils are deepened by trench-plowing and by sub- 
soiling. By trench-plowing, the common plow with 
a mould-board is made to enter the earth to an unu- 
sual depth, and to throw up a portion of the subsoil, 
covering with it the top-soil which is thrown under. 
A subsoil plow, on the contrary, only loosens the sub- 
soil, but does not lift it to the surface. 



THE DOUBLE MOULD-BOARD TRENCH-PLOW. 135 

"When a mixture of the subsoil with the surface tends 
to render the whole richer, trench-plowing is best ; but 
when the subsoil is of a more sterile character, it should 
be only loosened with the subsoil plow, and more cau- 
tiously intermixed with the richer portion above. 

It often happens that the subsoil plow is very use- 
ful in loosening the soil for the purpose of allowing the 
trench-plow to run more freely through it. 

THE DOUBLE MOULD-BOARD TRENCH-PLOW. 

This plow, sometimes called the Michigan Double 
Plow, is represented in Fig. 110. It has two mould- 



Fig, no 




boards on one beam. The forward or small one pares 
off the surface or sod, and throws it into the previous 
furrow, usually to a depth of three to five inches. The 
larger one follows closely, lifting the under-soil upon 
the top, and in sward land completely burying the sod 
with the mellow earth from below. This is the best 
implement for trench-plowing yet introduced into prac- 
tice, and with double the ordinary amount of team, 
will cut to a depth of nine to twelve inches. 



136 



MECHANICS. 



THE SUBSOIL PLOW, 

represented in Fig. Ill , consists of a narrow, horizon- 
Fig, in. 




Subsoil plow. 

tal, wedge-like share for loosening the earth, and con- 
nected with the beam by a strong plate of metal run- 
ning edgewise, so as to cause little resistance through 
the soil. This plow follows in the furrow after a com- 
mon plow, loosening but not lifting out the earth. The 
operation is shown in Fig. 112. The benefit of sub- 



Fig. 112. 




Subsoil plowing in the furrow of a common plow. 

soiling will last three or four years ; but it is of great 
importance that land be well underdrained, for if the 
earth becomes heavily soaked with water, it settles 
down into one compact mass, and the advantages of 
the operation are lost. 

fowler's draining plow. 

The mole-plow, for forming a small hollow passage 
beneath the soil, by means of a sharp iron plug forced 
through it at the lower end of a thin coulter, has been 



fowler's draining plow. 139 

already described. A great improvement has been 
made in this machine by the invention of the Draining 1 
plow, Fig. 113, opposite, which not only forms a hole 
through the subsoil, but fits into it at the same ope- 
ration earthen pipe or tubular tile, forming at once a 
perfect and durable under-drain. The pieces of tile or 
pipe, which are about a foot long, are strung on a rope, 
as shown in the foreground of the engraving. This 
rope is attached to the back end of the iron plug, and 
is drawn forward through the earth as the plug ad- 
vances, thus fitting the hole with tile as fast as it is 
formed. The only trace left on the surface of the earth 
is a narrow slit made by the coulter, an invisible drain 
being formed beneath it. 

The frame-work to which the coulter and plug are 
attached is drawn forward by an iron rope (made of 
twisted wire) wound upon a windlass or capstan work- 
ed by horses. Drains forty rods long are completed at 
one operation. A short piece of ditch is first dug for 
the admission of the plug, and strings of pipe, each fifty 
feet long, are successively added, and when done the 
whole of the rope is withdrawn. 

"When the surface of the ground is uneven, an in- 
genious contrivance preserves a straight and uniform 
slope to the drain. The coulter is worked up or down 
by the man who stands on the frame, by means of a 
wheel and screw, his eye being guided by a try-sight 
on the frame, and a cross-staff at the end of the field, 
set so as to give a proper slope. This machine, when 
tried in England, has been found to accomplish the 
work of draining with less than one half the ordinary 
expense. 



140 MECHANICS. 

THE PARING PLOW 

consists merely of a flat blade, which runs beneath the 
surface, shaving off the roots, but not moving the soil 
(Fig- 114). It is used in cutting turf for burning, 

Fig. 114. 




Paring plow. 

and for destroying thistles and other deep-rooted weeds. 
When made light for a single horse, it is sometimes 
used advantageously for cutting the grass and weeds 
between rows of corn. A two-horse paring plow has 
been lately constructed, in which the depth of cutting 
is accurately regulated by wheels placed on an axle 
like those of a cart. The cast-iron blade, which cuts 
about three feet wide, is raised or depressed by means 
of screws passing through the axle. Its chief utility 
is. in destroying grass and weeds before the sowing of 
broadcast crops. 

THE GANG PLOW. 

consists of three or four small mould-boards placed side 
by side (Fig-. 115), and is used for shallow plowing, or 
burying manure or seed on inverted sod, without dis- 
turbing the turf beneath. In those of the •best con- 
struction, the depth is regulated by wheels, and the 
breadth of the furrows by turning the cross-beam more 



THE HARROW. 

Fig. 115 



141 




Gang plow. 

or less obliquely, by means of a fixed contrivance for 
this purpose. 



SECTION II. 



PULVERIZERS. 



The fine pulverization of the soil, for the ready ex- 
tension of the fine roots of plants, and for the thorough 
intermixture of manure, is of great importance to the 
farmer. It is but partially accomplished by the plow, 
which crumbles the soil only so far as may be done by 
the act of turning it over. Hence additional imple- 
ments are needed for this 
purpose, among which are 
the harrow, the cultiva- 
tor, and the clod-crusher. 




THE HARROW 



Scotch or square harrow. 



The common form of 
the harrow is represented 
by Fig. 116, which con- 
sists of two parts hung 



142 



MECHANICS. 





together by hinges, so as to bend and fit an uneven 
surface of land, and to be folded for carrying in a cart 
or wagon. The dottted lines show the track of each 
Fig. 117. tooth. The Geddes Harrow, rep- 

resented in Fig. 117, is supe- 
rior to the square harrow on ac- 
count of its drawing more stead- 
ily from a centre, and its wedge- 
form frame passing more freely 
past any unusual obstruction. 
To prevent the central part from 
being lifted by the Fi ^ 118 - 
draught, the draught- 
Geddes Harrow. chain is fastened to the 

side-beams, as in Fig". 118. 

The teeth of harrows are often made too large and 
too few in number. Small and very numerous teeth 
pulverize the soil more finely and rapidly. They 
should be so placed that the corners, like wedges, 
and not the sides, may cut the soil in their onward 
progress ; and if the forward half of the teeth were 
made sharp and flat, similar to the coulter of a plow, 
they would not only run more easily, but cut and pul- 
verize clods more efficiently. This form of the teeth 
would admit of the use of cast-iron, which would be 
cheap and durable. 

The Norwegian Harrow, Fig. 119, is a new ma- 
chine for pulverizing the soil, which performs the work 
in a very perfect manner, by turning up instead of 
packing down the earth. Two rows of star-shaped 
tines play into each other, and produce a complete self- 



CULTIVATORS. 
Fig. 119. 



143 




Norwegian Harrow, kept from clogging by two cylinders of teeth 
playing into each other. 

cleaning action, preventing clogging even in quite ad- 
hesive soils. 



CULTIVATORS. 



The cultivator is used for loosening and pulverizing 
the soil, and for cutting and destroying weeds. The 
usual form is represented in Fig. 120, where the wheel 



Fig. 120. 




Common Cultivator. 



in front regulates the depth of the teeth. The width 
is altered by expanding or contracting the two outer 
beams. 

Yarious sorts of teeth are used, according to the na- 
ture of the work, and they are made of steel or cast- 



144 



MECHANICS. 



iron. The cast-iron teeth, represented in Fig. 120, 
are well adapted for cultivating the rows of Indian 
corn and other hoed crops, where the soil is already 
moderately mellow. For harder soils, the teeth should 
he in the form of claws, as shown in Fig. 121, their 

Fig. 121. 




Claw-toothed cultivator for hard ground. 

sharp, wedge-form points penetrating and loosening the 
earth with comparative ease. A very efficient culti- 
vator is made by using both kinds of teeth in the same 
implement, placing the claws forward for breaking the 
hard earth, and the broader teeth behind for stirring it. 
Steel plates, with sharp or " duck-feet" edges screw- 
ed at the lower extremities of the teeth, Fig. 122, are 

Fig. 122. 




useful for paring, or cutting the roots of weeds ; and 
formed like the mould-board of a plow, they are some- 
times used for throwing the mellow earth toward the 
row, or, when reversed, from it. 

In all cases, the teeth should be so long and the 
frame- work high enough above ground to allow room 



CLOD-CRUSHERS. 



145 



for the weeds to gather and fall off, even when the 
teeth are deepest in and the land the foulest. 

Two-horse cultivators are very useful in pulverizing 
the surface of inverted sod, and fitting it for the recep- 
tion of seed. They run on wheels, and an apparatus 
is attached for lowering or raising the frame-work and 
regulating the depth of the teeth. 

Garrett s Horse-hoe, an English invention, is a mod- 
ification of the cultivator, and is used for cultivating 
carrots and other root-crops in drills, cleaning eight or 
ten rows at once. It is furnished with sharp horizon- 
tal blades, which run beneath the surface, and shave 
off and destroy all the weeds within an inch of the 
rows of young plants. These rows, having been planted 
by means of a drilling-machine, are straight and per- 
fectly parallel, and the operator has only to watch one 
row and guide the blades for that row, the apparatus 
being so contrived that the blades for the other rows 
shall run at the same distance from them. 

Fig. 123 represents an end view of this implement. 



Fig. 123. 




Garrett's Horse-hoe — End view. 

a 



146 MECHANICS. 

It exhibits the apparatus by which the length of the 
axle is altered to suit all kinds of planting ; by which 
each hoe is kept independent of the others, so as to suit 
the inequalities of the ground, and by which they can 
be set any width, from seven inches to thirty. It 
shows the oblique angle at which they run — this obliq- 
uity being easily altered to any desired degree : this is 
effected by a movement of the upper handle represent- 
ed in the figure. By the lower handle the whole is 
accurately guided. It is said that two men, one to lead 
the horse, and the other to guide the implement, will 
dress ten acres of root-crops in a single day, and that it 
has proved eminently a labor-saving machine. 

CLOD-CRUSHERS. 

In clayey soils, clods are often formed in abundance 
during the process of cultivation. These become very 
hard in dry weather, and prevent the proper extension 
of the fine roots of pl?nts in search of nourishment, and 
also the intermixture of manure with the soil, without 
which it has been found that two thirds or even three 
fourths of the value of manure is lost to growing crops. 

Different modes of pulverizing the clods have been 
adopted. The simplest is the " drag -roller," repre- 
sented in Fig. 124. It is made of a log or portion of 

Fig. 124. 




Clod-crusher. 

a hollow tree, into which a common two-horse wagon 



CLOD-CRUSHERS. 



147 



tongue has been fitted, by which it is dragged over 
the ground without rolling, grinding to powder, in 
its progress, every clod over which it passes. The 
greater the diameter of the log, the less will be the lia- 
bility of its clogging by gathering the clods before it. 
It may also be made of a half log with the round side 
downward. Fig. 125 represents a similar implement 



Fig. 125. 




One-horse Clod-crusher. 

for one horse, and is used for working between the 
rows of corn in cloddy ground. 

The use of these simple implements, by reducing 
rough fields to a condition as mellow as ashes, has in 
some instances been the means of doubling the crop. 
It is necessary that the soil be dry when they are used, 
to prevent its packing together. 

CrosskilVs Clod-crusher is a more powerful and 

. Fig. 126. 




CrossltilVs Clod-crusher. 



148 



MECHANICS. 



more costly implement (Fig: 126). It consists of 
about two dozen circular cast-iron disks, placed loosely 
upon an axle, so as to revolve separately. Their outer 
circumference is formed into teeth, which crush and 
grind up the clods as they roll over the surface of the 
field. Every alternate disk has a larger hole for the 
axle, which causes it to rise and fall while turning 
over, and thus prevent the disks from clogging. It 
can he used only when the ground is dry. 



SECTION III. 
SOWING-MACHINES. 

Sowing-machines, for wheat and other grains, pos- 
sess great advantages over hand-sowing. All the seed 
being deposited by them at nearly a uniform, depth, 
and completely covered with earth, it vegetates and 
grows evenly, and the plants are uniformly strong and 
vigorous. A less quantity of seed is required, and the 
crop is heavier. 

Small seeds, such as carrots and turnips, can be 
sown evenly and rapidly only by means of drills adapt- 
ed to these seeds, and hence drilling-machines are in- 
dispensable in the cultivation of such root-crops. 

A great number of different drills have been made 
for sowing grain, the general principles of which can 
be only noticed in this treatise. The seed is delivered 
by means of a revolving cylinder, in the surface of 
which small regular cavities have been made, which 
constantly carry off and drop measured portions of the 
grain. The motion of this cylinder is increased or less- 
ened by means of wheel- work, according to the quan- 




Gram-drilling Machine. 



SOWING-MACHINES. 



151 



tity of seed to be sown. As soon as the seed drops 
from the revolving cylinder, it falls down either through 
a hollow coulter, or through a tube which opens just 
behind a coulter, into the bottom of the furrow, and is 
immediately buried by the earth falling back upon it 
after the coulter has passed. 

Drills for sowing small seeds are usually furnished 
with a spindle having circular brushes, which press 
the bottom of the hopper, and force the seed through 
small holes made for its escape. 

For planting corn, beans, and other crops cultivated 
in drills and hills, the machines are so regulated as to 
drop either in hills or in uniform rows, and they do 
the work more evenly than when performed by hand. 
The coulters or tubes for depositing the seed should, 
in all machines of this kind, be made sharp and not 
rounded on the forward part, that the draught may be 
easier. 

A simple grain-drill is represented in operation by 
Fig. 127, and one of more finished construction by 
Fig. 128, showing the cog-wheel gearing for regulat- 
ing the quantity of seed, and the chains for lifting up 
the discharging tubes from the ground when not in use. 

A very simple 
machine for sow- 
ing grass, as well 
as other small 
seed, by hand, is 
shown in the an- 
nexed figure. It 
consists of a light 
trough, contain- 



Fig. 129. 




-"neMts-v*-**" 



152 MECHANICS. 

ing the seed, which is distributed through holes in the 
zinc bottom by the vibrations of a notched rod, and 
any desired quantity of seed accurately regulated. 

HORSE-RAKES. 

In all labor-saving contrivances, the greatest advant- 
age is gained where the work originally performed by 
the hand is light, or where much exertion of strength 
is not required. An example of this kind occurs in the 
use of hand-drills for sowing small seeds, such as tur- 
nips and carrots. These, when planted by the unas- 
sisted hand, require but little power, but the operation 
is very slow. A hand-drill enables the laborer to apply 
his whole strength profitably, with an increase in ef- 
fect of at least forty or fifty times. A similar advant- 
age is gained by the use of the horse-rake, where the 
full strength of a horse is made to accomplish the 
moderate labor of the hand-rake, and to perform an 
amount equal to at least ten men. "With the simplest 
form of the horse-rake, sixteen acres of heavy hay have 
been collected by one horse in a day, and with the re- 
volving-rake, twenty to twenty-five acres. 

The simplest form of the horse-rake is represented in 
Fig. 130. It is made of a piece of strong scantling 
three inches square, tapering slightly toward the ends, 
for the purpose of combining strength with lightness, 
and in which are set horizontally about fifteen teeth, 
twenty-two inches long, and an inch by an inch and 
three fourths at the place of insertion, tapering on the 
under side, with a slight upward turn at the points, to 
prevent their running into the ground. The two outer 
teeth should be cut off to about one third their first 



HORSE-RAKES. 

Fig. 130. 



153 




Simple Horse-rake. 



length, and draught-ropes attached. If they are too 
short, the teeth will he hard to guide ; if too long, the 
rake is unloaded with difficulty. Handles serve to 
guide the teeth, to lift the rake from the ground in 
avoiding obstructions, and to empty the accumulated 
hay. 

In using this rake, the teeth, instead of moving on 
their points as in the common hand-rake, run flat upon 
the ground, passing under and collecting the hay. 
When full, the horse is stopped, the handles thrown for- 
ward, the rake emptied and lifted over the winrow thus 
formed. The winrows are made at right angles to the 
path of the rake, as each load is deposited opposite the 
last heap formed in previously crossing the meadow. 
A few hours' practice enables any one to use this rake 
without difficulty ; the only skill required is to keep the 
teeth under the hay and above the ground. "When 
small obstructions occur, the handles are depressed, and 
the points of the teeth rise and pass freely. Over large 
obstructions, the rake must be lifted. By shortening 
the teeth, it may be used on the roughest ground. 

In addition to raking, this implement may be em- 
G2 



154 



MECHANICS. 



ployed for sweeping the hay from the winrow and 
drawing it to the stack. It is also useful for cleaning 
up the scattered hay from the meadow at the close of 
the work, for raking grain-stubble, and for pulling and 
gathering peas. 

Its chief advantages over other horse-rakes are its 
simplicity, cheapness, and little liability to get out of 
order — adapting it to small farms — and its superior 
fitness for uneven surfaces. If made of the toughest 
wood, and with the proper taper in the main parts for 
lightness and strength, according to the principles al- 
ready pointed out in a previous chapter, it is easily 
lifted, and its use not attended with severe labor. 

The Revolving 1 Horse-rake, Fig. 131, is similar in 

Fig. 131. 




Revolving Horse-rake. 



its mode of operation, possessing, however, the great 
advantage of unloading without lifting the rake or stop- 
ping the horse. It has a double row of teeth, pointing 
each way, which are brought alternately into use as 
the rake makes a semi-revolution at each forming win- 
row in its onward progress. They are kept flat upon 
the ground by the pressure of the square frame on their 
points beneath the handles ; but as soon as a load of 
hay has collected, the handles are slightly raised, throw- 



HORSE-RAKES. 



155 



ing this frame backward off the points, and raising 
them enough for the forward row to catch the earth. 
The continued motion of the horse causes the teeth to 
rise and revolve, throwing the backward teeth fore- 
most over the winrow. In this way each set of teeth 
are alternately brought into operation. 

The cost of the revolving rake, well made, is about 
four times that of the simple horse-rake, but on large 
meadows it possesses the superior advantages of expe- 
dition and ease in working. 

The Spring-tooth Horse-rake, Fig. 132, has been 




Spring-tooth Horse-rake. 

much used, and has proved a valuable implement. The 
teeth are made of stiff, elastic wire, on the points of 
which the rake runs, and not on the flat sides, as in the 
two already described. They bend in passing an ob- 
struction, and spring back again to their place. This 
rake is unloaded by simply lifting the handles, which 
is easily done, the rake being light, and about one half 
the weight being sustained by the horse. It is pecu- 



156 MECHANICS. 

liarly adapted to raking stubble, its upright teeth pre- 
venting the collection of portions of the soil with the 
straw. 

All horse-rakes used on meadows are not only use- 
ful by the immediate saving of labor, but sometimes 
still more so by the expedition with which a crop of 
well-dried hay may be rescued from an approaching 
storm. 

MOWING AND REAPING MACHINES. 

The cutting part of all the best mowers and reapers 
F »g- 133 - made at the present day 

a ■/C^^^ / ^- y/ ^^l^L consists of a serrated 

blade, as shown at a 

* (\ f)_/L_A- (^ 133 )' wMch P ass - 

— I - l l es through narrow slits 

in each of the fingers shown in b, forming, when thus 
united, the cutting apparatus, as exhibited in the an- 
nexed figure of Ketchuvi's Mowing-machine (Fig. 
134). When the machine is used, the motion of the 

Fig. 134. 




Ketchum's Mowing-machine. 



wheel on which the machine runs is multiplied by 
means of the cog-wheels, imparting quick vibrations 



MOWING AND REAPING MACHINES. 



157 



endwise to this blade, shearing off the grass smoothly 
as it advances through the meadow, like a large num- 
ber of scissors in exceedingly rapid motion. Fig. 135 

Fig. 135. 




Back view of KetchurrCs Mower in operation. 

represents Ketchum's mower in operation as seen from 
behind, cutting an even swath five feet wide as fast as 
the horses advance. 

In the mowing-machine the cutting apparatus is 
narrow, causing the newly-cut grass to fall evenly be- 
hind it, covering the whole surface of the ground. The 
reaping-machine is similar in construction, with the 
addition of a platform for holding the grain as it falls, 
as shown in the figure of Hussey's Reaper (Fig. 136). 

Fig. 136. ' 




Hussey's Reaping-machine. 



158 MECHANICS. 

As the straw collects on this platform, it is raked off 
in successive bunches for hinding by a man who rides 
on the machine for this purpose. 

Most reaping-machines are provided with a revolv- 
ing reel, which strikes backward against the standing 
grain, holds it there while the blade is cutting, and 
throws it backward on the platform. This reel is dis- 
tinctly shown in the representation (Fig. 137) of Man- 
Fig. 137. 




f 

Manny's Mowing and Reaping Machine, showing the reel distinctly. 

ntfs Mowing and Reaping Machine, where the cut- 
ting blade is placed midway between the forward and 
back wheels. 

Mowing machines require but one man for their 
management, who merely drives the horses that draw 
it. Reapers, as usually made, require another man be- 
sides the driver, to rake off the bunches of cut grain, 
which is severe labor. Various self-raking contriv- 
ances have been tried to obviate this labor, one of the 
most ingenious and best of which is Atkins 1 Self-raker, 
represented by Fig. 138, and sometimes called the 
Automaton Raker. An ingenious piece of mechanism 
causes the rake to sweep the platform, and presses the 
fallen grain against another rake, when both of them, 
with the bundle of grain firmly inclosed, swing round 
behind, and then open wide, and drop it on the ground 
ready for binding. It may be so regulated as to drop 



THE KNEE-JOINT POWER. 
Fig. 138. 



Atkins' Automaton Reaper in operation. 



159 




the bunches more frequently where the crop is heavy, 
or more remotely where it is light. 



SECTION IV. 

THE KNEE-JOINT POWER APPLIED TO MACHINES. 

The knee-joint or toggle-joint is usually regarded 
Fig. 139. as a compound lever, and consists of two 
rods connected by a turning joint, as rep- 
resented in Fig. 139. The outer end of 
one of the levers is fixed to a solid beam, 
and the other connected with a movable 
block. When the joint a is forced in the 
direction indicated by the arrow, it pro- 
Knee-joint power, duces a powerful pressure upon the mov- 
able block, which increases as the lever approaches a 
straight line. This is easily understood by the rule of 
virtual velocities, for the force moves with a velocity 
many times greater than the power given to the block, 
and this relative difference increases as the joint is 
made straighter. 

This power is made use of in the lever printing-press, 
where the greatest force is given just as the pressure 
is completed. Another example occurs in the Lever 




160 



MECHANICS. 



Washing-machine (Fig. 140), which is worked by 
the alternating motion of the handle, A, pressing a 
swinging-hoard, perforated with holes, with great force 

Fig. 140. 




Lever Washing-machine. 

against the clothes next to one side of the water- 
box. Like the printing-press, this machine exerts the 
greatest power just as the motion of the lever is 
completed, and at the time it is most needed. The 
same principle is exhibited in Kendall's Cheese-press 
(Fig. 141), where the lever and the wheel-and-axle 
are combined with the two knee-joints, one on each 
side of the press, drawing down a cross-beam upon the 
cheese with a greatly multiplied power. Emery's 
Hay-press, for compressing hay into bales for distant 
conveyance, is another example (Fig. 142). The hay 
is thrown into a space in a strong box by opening the 
top doors, and when trodden down, the doors are closed 
and secured by buttoning down the cross-bars. Horse- 



THE KNEE-JOINT POWER. 
Fig. 141. 



161 




Kendall's Cheese-press. 
Fig. 142. 




Emery's Hay-press. 



power is then applied to chains, which draw down the 



162 MECHANICS. 

raised levers, operating on a knee-joint, and compress- 
ing the hay into a small and compact mass, the great- 
est force being given when most needed, at the termi- 
nation of the pressure. Side-doors are then thrown 
open, and the hay secured by bands and taken out. 
Two hundred and fifty pounds of hay may be thus re- 
duced to a space of sixteen cubic feet, or a little more 
than half a cubic yard, by a single horse ; and several 
tons may be pressed in a day. Dederick's improve- 
ment in this press consists in placing the levers at one 
end only, compressing the hay into the other end, and 
thus simplifying the machine. Double levers, press- 
ing equally against the upper and lower part of the 
slide or piston, keep it always upright and even, al- 
though the hay may be unequally compact. These 
double levers are connected and kept parallel by con- 
necting hinged bars. 

The power exerted by a rolling-mill, where bars of 
iron are flattened in their passage between two strong 
rollers, is precisely like that of the knee-joint. The 
only difference is, that the rollers, which may be con- 
sidered as a constant succession of levers coming into 
play as they revolve, are both 
fixed, and consequently the 
bar has to yield between them 
{Figure 143). The greatest 
power is exerted just as the 
bar receives the last pressure 
from the rollers. The most 
powerful and rapidly-working 

Principle of the knec-jomt in the l i J 

roiiing-miii. straw-cutters are those which 

draw the straw or hay between two rollers, one of 




THE KNEE-JOINT POWER. 



ies 



which is furnished with knives set around it parallel 
with its axis, and cutting on the other, which is cover- 
ed with untanned ox-hide (Fig: 144). The only de- 
Fig. 144. 




Fig 146. 



feet in this machine is its inability to cut shorter than 
one inch in length, which is not sufficient for corn- 
stalks and other coarse fodder. 

Dick's Cheese-press (Fig. 145, 
on the following page) operates on 
a similar principle. Figure 146 
shows the structure of its working 
part, the dotted lines indicating the 
position of the lever, which is in- 
serted into a roller or axle, and, by 
turning, drives the movable iron 
blocks asunder, and raises the 
cheese against the broad screw- 
head above, as shown in Fig. 145. In Fig. 146, the 
raised lever shows that the blocks are at first near to- 
gether, but are crowded asunder as the lever is press- 
ed downward. This cheese-press is made of cast-iron, 




164 



MECHANICS. 
Fig. 145. 




Dick's cast-iron Cheese-press. 



and has great power ; to try it, weights were increased 
upon the lever, until the iron frame broke with a force 
equal to sixteen tons. 



ENDLESS-CHAIN POWERS. 

A convenient and compact machine for applying ani- 
mal power is by means of the endless chain, working 
in the position of an inclined plane, as represented in 
the annexed cut (Fig. 147), where the weight of a 
Jarge dog is used for driving a churn-dasher. The 
platform on which the animal stands is formed of strips 
of light wood riveted to two India-rubber straps, and 
their constant downward motion turns the fly-wheel, 
to which a rod is attached for working the dasher. 



ENDLESS-CHAIN POWERS. 
Fig. 147. 



165 




Churn worked by dog-power. 

The same principle has been lately adopted with 
great success in the application of horse-power to driv- 
ing thrashing-machines, sawing wood, and to various 
other purposes. Instead of India-rubber straps, strong 
cast-iron chains are used, which are made to run 
smoothly and with very little friction over a succession 
of small iron wheels, which support the weight of the 
horses on the moving platform (Fig-. 148, on the fol- 
lowing page). 

The power of these machines, and the amount of 
friction in running them, may be easily ascertained by 
the rule, already given in a former part of this work, 
for determining the power of the inclined plane ; for 
the only difference between the endless-chain and a 
common inclined plane is, that in one the plane is 
fixed, and the body moves up its surface, and in the 
other the plane itself moves downward, and the weight 
or animal upon it remains stationary. The same prin- 



166 



MECHANICS. 



ciple applies in both 

cases. 

First, to ascertain 

the friction, let the 

platform he placed on 
^ a level, with the horse 
| upon it ; then gradual- 
? ly raise the end until 

BO •> 

| the weight of the horse 
| will just give it mo- 
tion. This will show 
the precise amount of 
the friction ; for if the 
end be elevated one 
twentieth of its length, 
then the friction is one 
twentieth the weight 
of the horse and plat- 
form. 

Secondly, to deter- 
mine the power, when 
the end is still further 
raised, measure the 
difference between the 
height thus given and the length of the platform. If, 
for instance, the height of the inclination is one eighth 
of its length, and the horse is found to weigh eight 
hundred pounds, then the power is one hundred pounds, 
or one eighth the weight of the horse. 

This rule will not, however, apply, when the draught 
of the horse is added to its weight ; for it usually hap- 
pens that the weight alone is not sufficient, without 




APPLICATION OF LABOR. 167 

placing the platform in too steep a position for a horse 
to work comfortably. He is therefore attached to a 
whipple-tree placed on the frame of the machine, so 
that in drawing he pushes the platform backward with 
his feet. In this case, the power can be only ascer- 
tained by the use of the dynamometer, already de- 
scribed. 



SECTION V. 
APPLICATION OP LABOR. 

Most of the moving powers applied by the farmer to 
accomplish labor are the exertions of animal strength. 
A principal object of the preceding pages is to point out 
how this strength can be applied in the most econom- 
ical manner, and to aid in the substitution of cheap 
horse-power for more costly human labor. It will 
doubtless contribute to the end to exhibit the relative 
efficiency of each, as well as the results of strength 
differently applied. 

The amount of work which any machine is capable 
of performing is denoted by comparing this amount 
with the power of a single horse ; hence the common 
expressions of twenty, or fifty, or a hundred horse- 
power engines. The strength of different horses varies 
greatly, but the expression, as commonly understood, 
indicates a force equivalent to raising or pressing with 
a force equal to 150 pounds 20 miles a day, at the rate 
of two and a half miles an hour. This is the same as 
33,000 pounds raised one foot in one minute. The re- 
sults of numerous experiments in different places give 
the actual power of the average of horses at somewhat 



168 MECHANICS. 

less than this ; and there is no doubt that, for most of 
the farm-horses of this country, the result would he 
considerably less. The power of a strong English 
draught-horse has been ascertained to be about 143 
pounds for 22 miles a day, at 2| miles an hour. Many 
American horses are scarcely more than half as strong. 
The strength of a man, working at the best advantage, 
is estimated at one fifth that of a horse. As the speed 
of a horse increases, his strength of draught diminishes 
very rapidly, till at last he can only move his own 
weight. This is owing to three reasons : first, the load 
moves over a greater space in a given time, and if, for 
instance, the speed be doubled, half the load only can 
be carried with the same quantity of power, according 
to the law of virtual velocities ; secondly, the horse 
has to carry the full weight of his body, whatever his 
speed may be, and the force expended for tins purpose 
alone must, therefore, be doubled as the speed is 
doubled ; thirdly, a very quick and unaccustomed mo- 
tion of the muscles is in itself more fatiguing than the 
ordinary or natural velocity. 

The following table shows the amount of labor a 
horse of average strength is capable of performing in a 
day at different degrees of speed, on canals, rail-roads, 
and on turnpikes. The force of draught is estimated 
at about 83 pounds. This is considerably less than 
the horse-power used in estimating the force of machin- 
ery, but it is as much as an ordinary horse can exert 
without being improperly fatigued with continued ser- 
vice: 



APPLICATION OF LABOR. 169 



Velocity 
per hour. 


Duration of the 
day's work. 

Hours. 


Wor/t accomplished for one day, 
one "mile. 


in tons, drawn 


Miles. 


On a canal. 


On 


a rail-road. 


On a turnpike. 


2£ 


11* 


520 




115 


14 


3 


8 


243 




92 


12 


3£ 


5 tV 


153 




82 


10 


4 


4^ 


102 




72 


9 


5 


2 9 
TiT 


52 




57 


7.2 


6 


2 


30 




48 


6 


7 


1* 


19 




41 


5.1 


8 


1* 


12.8 




36 


4.5 


9 
10 


9 
1 


9 
6.6 




32 

28.8 


4 
3.6 



From trie preceding table it will be seen that a horse, 
at a moderate walk, will do more than four times as 
much work on a canal as on a rail-road ; but the re- 
sistance of the water increases as the square of the ve- 
locity, and therefore when the speed reaches five miles 
an hour, the rail-road has the advantage of the canal. 
On the rail-road and turnpike the resistance is about 
the same, whether the speed be great or little, the 
chief loss with fast driving resulting from the increased 
difficulty with which the horse carries forward his own 
body, which weighs from 800 to 1200 pounds. The 
table also shows that, when it becomes necessary to 
drive rapidly with a load, it should be continued but 
for a very short space of time ; for a horse becomes as 
much fatigued in an hour, when drawing hard at ten 
miles an hour, as in twelve hours at two and a half 
miles an hour ; because, when a boat is driven through 
the water, to double its velocity not only requires that 
twice the amount of water should be moved or dis- 
placed in a given time, but it must be moved with 
twice the velocity, thus requiring a four-fold force. 

The muscular formation of a horse is such that he 
H 



170 MECHANICS. 

will exert a considerably greater force when working 
horizontally than up a steep inclined plane. On a 
level, a horse is as strong as five men, but up a steep 
hill he is less strong than three ; for three men, carry- 
ing each 100 pounds, will ascend faster than a horse 
with 300 pounds. Hence the obvious waste of power 
in placing horses on steeply-inclined tread- wheels or 
aprons. The better mode is to allow them to exert 
their force more nearly horizontally, by being attached 
to a fixed portion of the machine. For the same rea- 
son, the common opinion is erroneous that a horse can 
draw with less fatigue on an undulating than on a level 
road, by the alternations of ascent and descent calling 
different muscles into play, and relieving each in turn ; 
for the same muscles are alike exerted on a level and 
on an ascent, only in the latter case the fatigue is much 
greater than the counterbalancing relief. Any person 
may convince himself of the truth on this subject by 
first using a loaded wheel-barrow or hand-cart for one 
day on a level, and for the next up and down a hill ; 
bearing in mind, at the same time, that the human 
body is better fitted for climbing and descending than 
that of a horse. 

A draught-horse can draw 1600 pounds 23 miles in 
a day on a good common road, the weight of the car- 
riage included. On the best plank-road he will draw 
more than twice as much. 

A man of ordinary strength exerts a force of 30 
pounds for 10 hours a day, with a velocity of 2£ feet 
per second. He travels, without a load, on level ground, 
during 8£ hours a day, at the rate of 3.7 miles an hour, 
or 31 \ miles a day. He can carry 111 pounds 11 



APPLICATION OF LABOR. 171 

miles a day. He can carry in a wheel-barrow 150 
pounds 10 miles a day. 

Well-constructed machines for saving human labor 
by means of horse-labor, when encumbered with little 
friction, will be found to do about five times as much 
work for each horse as where the same work is per- 
formed by an equal number of men. For example : an 
active man will saw twice each stick of a cord of wood 
in a day. Six horses, with a circular saw, driven by 
means of a good horse-power, will saw five times six, 
or thirty cords, working the same length of time. In 
this case the loss by friction is about equal to the ad- 
ditional force required for attendance on the machine. 

Again : a man will cut with a cradle two and a half 
acres of wheat in a day. A two-horse reaper should 
therefore cut, at the same rate, ten times two and a 
half, or twenty-five acres. This has not yet been ac- 
complished. We may hence infer that the machinery 
for reaping has been less perfected than for sawing 
wood. It should, however, be remembered, that great 
force is exerted, and for many hours in a day, in cut- 
ting wheat with a cradle, and therefore a little less 
than twenty-five acres a day may be regarded as the 
maximum attainment of good reaping-machines, when 
they shall become perfected. 

Applying the same mode of estimate, a horse-culti- 
vator will do the work of five men with hoes, and a 
two-horse plow the work of ten men with spades. A 
horse-rake accomplishes more than five men, because 
human force is not strongly exerted with the hand-rake. 

In using different tools, the degree of force or press- 
ure applied to them varies greatly with the mode in 



172 MECHANICS. 

which the muscles are exerted. The following tahle 
gives the results of experiments with human strength, 
variously applied, for a short period : 

Force of the hands Force of the tool 
on the tool. on the object. 

With a drawing-knife 100 lbs. 100 lbs. 

" a large auger, both hands 100 " about 800 " 

" a screw-driver, one hand 84 " 250 " 

" a bench-vice handle 72 " about 1000 " 

" a windlass, with one hand 60 " 180 to 700 " 

" a hand-saw 36 " 36 " 

" a brace-bit, revolving 16 " 150 to 700 " 

Twisting with thumb and fingers, but- 
ton-screw, or small screw-driver. ... 14 " 14 to 70 " 

The force given in the last column will, of course, 
vary with the degree of leverage applied ; for example, 
the arms of an auger, when of a given length, act with 
a greater increase of power with a small size than 
with a large one. This degree of power may he calcu- 
lated for an auger of any size, by considering the arms 
as a lever, the centre screw the fulcrum, and the cut- 
ting-blade as the weight to be moved. The same 
mode of estimate will apply to the vice-handle, the 
windlass, and the brace-bit. 

Every one is aware that a heavy weight, as a pail 
of water, is easily lifted when the arm is extended 
downward, but with extreme difficulty when thrown 
out horizontally. In the latter case, the pail acts with 
a powerful leverage on the elbow and shoulder-joint. 
For this reason, all kinds of hand-labor, with the arms 
pulling toward or pushing directly from the shoulders, 
are most easily performed, while a motion sidewise or 
at right angles to the arm is far less effective. Hence 
great strength is applied in rowing a boat or in using 



MODELS OF MACHINES. 173 

a drawing-knife, and but little strength in turning a 
brace-bit or working a dasher-churn. Hence, too, the 
reason that, in turning a grindstone, the pulling and 
thrusting part of the motion is more powerful than 
that through the other parts of the revolution. This 
also explains why two men, working at right angles to 
each other on a windlass, can raise seventy pounds 
more easily than one man can raise thirty pounds 
alone. This principle should be well understood in the 
construction or selection of all kinds of machines for 
hand labor. 



SECTION" VI. 
MODELS OF MACHINES. 



Serious errors might often be avoided, and some- 
times gross impositions prevented, by understanding 
the difference between the working of a mere model, 
on a miniature scale, and the working of the full-sized 
machine. It is a common and mistaken opinion that 
a well-constructed model presents a perfect representa- 
tion of the strength and mode of operation of the ma- 
chine itself. 

When we enlarge the size of any thing, the strength 
of each part is increased according to the square of the 
diameter of that part; that is, if the diameter is twice 
as great, then the strength will be four times as great ; 
if the diameter is increased three times, then the 
strength will be nine times, and so on. But the weight 
increases at a still greater rate than the strength, or 
according to the cube of the diameter. Thus, if the 
diameter be doubled (the shape being similar), the 



174 MECHANICS. 

weight will be eight times greater ; if it he tripled, 
the weight will be twenty-seven times greater. Hence, 
the larger any part or machine is made, the less able 
it becomes to support the still greater increasing 
weight. If a model is made one tenth the real size 
intended, then its different parts, when enlarged to full 
size, become one hundred times stronger, but they are 
a thousand times heavier, and so are all the weights 
or parts it has to sustain. All its parts would move 
ten times faster, which, added to their thousand-fold 
weight, would increase their inertia and momentum 
ten thousand times greater. For this reason, a model 
will often work beautifully when made on a small 
scale ; but when enlarged, the parts become so much 
heavier, and their momentum so vastly greater, from 
the longer sweep of motion, as to fail entirely of suc- 
cess, or to become soon racked to pieces. 

This same principle is illustrated in every part of 
the works of creation. The large species of spiders 
spin thicker webs, in comparison with their own diam- 
eter, than those spmi by the smaller ones. Enlarge a 
gnat until its whole weight be equal to that of the 
eagle, and, great as that enlargement would be, its 
wing will scarcely have attained the thickness of writ- 
ing-paper, and, instead of supporting the weight of the 
animal, would bend down from its own weight. The 
larger spiders rarely have legs so slender in form as 
the smaller ones ; the form of the Shetland pony is quite 
different from that of the large cart-horse ; and the 
cart-horse has a slenderer form than the elephant. 

The common flea will leap two hundred times the 
length of its own body, and the remark has been some- 



MODELS OF MACHINES. 175 

times made that a man equally agile, with his present 
size, would vault over the highest city -steeple, or across 
a river as wide as the Hudson at Albany. Now, if the 
flea were increased in size to that of a man, it would 
become a hundred thousand times stronger, but thirty 
million times heavier ; that is, its weight would be- 
come three hundred times greater than its correspond- 
ing strength. Hence we may infer that the enlarged 
flea would be no more agile than a man ; or that, if a 
man were proportionately reduced to the size of a flea, 
he could leap to as great a distance. 

All this serves to illustrate in a striking manner the 
distinction between models and machines. 



PART II, 

HYDRODYNAMICS.* 

Hydrostatics! treats of the weight and pressure of 
liquids when not in motion ; Hydraulics, t of liquids in 
motion, as, conducting water through pipes, raising it 
by pumps, &c. ; and Hydrodynamics includes both, by 
treating of the forces of the liquids, whether at rest or 
in motion. 



CHAPTER I. 
hydrostatics. 



SECTION I. 
UPWARD PRESSURE. 

A remarkable property of liquids is their pressure 
in all directions. If we place a solid body, as a stone, 
in a vessel, its weight will only press upon the bottom ; 
but if we pour in water, the water will not only press 
upon the bottom, but against the sides. For, bore a 
hole into the side, and the side pressure will drive out 
the water in a stream ; or, bore small holes into the 
sides and bottom of a tight wooden box, stopping them 

* From two Greek words, hudor, water, and dunamis, power, 
t From two Greek words, hudor, water, and statos, standing, or at 
rest. % From two Greek words, hudor, water, and aulos, a pipe. 



UPWARD PRESSURE. 177 

with plugs ; then press this box, empty, "bottom down- 
ward, into water, allowing none to run in at the top. 
Now draw one of the side plugs, and the water will he 
immediately driven into the box by the pressure out- 
side. If a bottom plug be drawn, the water will im- 
mediately spout up into the box, showing the pressure 
upward against the bottom. Hence the pressure in 
all directions, upward, sideways, and downward, is 
proved. 

The upward pressure of liquids may be shown by 
pouring into one end of a tube, bent in the shape of the 
letter U, enough water to partly fill it ; the upward 
pressure will drive it up the other side till the two 
sides are level. 

On this principle depends the art of conveying water 
in pipes under ground, across valleys. The water will 
rise as high on the opposite side the valley as the spring 
which supplies it. The ancient Romans, who were 
unacquainted with the manufacture of strong cast-iron 
pipes, conveyed water on lofty aqueducts of costly ma- 
sonry, built level across the valleys. Even at the pres- 
ent day, it has been deemed safest to build level aque- 
ducts for conveying great bodies of water, as in very 
large pipes the pressure would be enormous, and might 
result in violent explosions. 

If the valleys are deep, the pipes must be correspond- 
ingly strong, because, the higher the head of water, the 
greater is the pressure. For the same reason, dams 
and large cisterns should be strongest at bottom. Res- 
ervoirs made in the form of large tubs require the 
lower hoops to be many times stronger or more numer- 
ous than the upper. 

H2 



178 HYDRODYNAMICS. 

MEASUREMENT OF PRESSURE AT DIFFERENT HEIGHTS. 

The amount of pressure which any given height of 
water exerts upon a surface below may be understood 
by the following simple calculation : 
. If there be a tube one inch square (with a closed 
end), half a pound of water poured into it will fill it to 
a height of fourteen inches ;* one pound will fill it 
twenty-eight inches ; two pounds, fifty-six inches ; ten 
Fig. 149. pounds, twenty -three feet; twenty 

•••-2 lbs. 56 in. pounds, forty-six feet, and so on. 
Now, as the side pressure is the same 
as the pressure downward for the 
„ ... ... . same head of water, the same column 

- t/?. lbs. 42 m. _ ' 

will, of course, exert an equal press- 
ure on a square inch of the side of 
the tube. Or, if the tube be bent, as 

lib 28 in. shown in the annexed figure {Fig. 

149), the pressure upward on the end 
of the tube, at a, will be the same for 
the various heights. 
1/2lb-14::La * Now, as the pressure of a column 
fifty feet high is about twenty-two 
pounds on a square inch, the pressure 
on the four sides is equal to eighty- 
eight pounds for one inch in length. 
Hence the reason that considerable 
strength is required in tubes which have much head 
of water, to prevent their being torn open by its force. 

* This is nearly correct, for a cubic foot (or 1728 cubic inches) of 
water weighs 62 lbs. Consequently, one pound will be 27.9 cubic 
inches, and will fill the tube nearly 28 inches high. 



SPRINGS AND ARTESIAN WELLS. 179 

DETERMINING THE STRENGTH OF PIPES. 

The question may now arise, and it is a very import- 
ant one, How thick must be a lead tube of this size to 
prevent danger of bursting with a head of fifty feet, or 
of any other height ? To answer it, let us turn to the 
table of the Strength of Materials in a former part of 
this work, where we find that a bar of cast lead one 
fourth of an inch square will bear a weight of fifty -five 
pounds. If the tube be only one sixteenth of an inch 
thick, one inch of one of its sides will possess an equal 
strength, that is, will bear fifty-five pounds only, and 
the tube would consequently burst with fifty feet head. 
If one tenth of an inch thick, the tube would just bear 
the pressure, and, to be safe, should be about twice as 
thick, or one fifth of an inch. Half this thickness 
would be sufficient for twenty-five feet of water, which 
would require to be doubled for one hundred feet. A 
round tube, one inch in diameter, having less surface 
to its sides, would be about one third stronger. A tube 
twice the diameter would need twice the thickness ; 
or if less in diameter, a proportionate decrease in thick- 
ness might take place. If, instead of cast lead, milled 
lead were used, the tube would be nearly four times 
as strong, according to the table of the strength of ma- 
terials already referred to. 

SPRINGS AND ARTESIAN WELLS 

Result from the upward pressure of water. Rocks are 
usually arranged in inclined layers {Fig. 150, p. 180), 
and when rain falls upon the surface, as at c d, it sinks 
down in the more porous parts between these layers, 



180 



HYDRODYNAMICS. 




to c. If the layers happen to be broken in any place 
below, the water finds its way up through the crevices 
by the pressure of the head above, and forms springs. 
If there are no openings through the rocks, deep borings 
are sometimes made artificially, through which the wa- 
ter is driven up to the surface, as at a, forming what 
are termed Artesian Wells. The head of water which 
supplies them may be many miles distant, the place 
of discharge being on a lower level. It has sometimes 
been found necessary to bore more than a thousand 
feet downward before obtaining water which will flow 
out freely at the surface of the earth. 



SECTION II. 
DETERMINING THE PRESSURE ON GIVEN SURFACES. 

The pressure of liquids upon any given surface is 
Fig 151 always exactly in proportion 

to the height, no matter what 
the shape of the vessel may 
be. If, for instance, the ves- 
sel a {Fig. 151), be one inch 
in diameter, and the vessel b 
be three inches in diameter, 



u 




,3 






! 






^f • 


! 










nm 


j 




DETERMINING THE PRESSURE ON GIVEN SURFACES. 181 

the water being equally high in both, the pressure on 

the whole bottom of b will be nine times as great as 

on the bottom of a ; or any one inch of the bottom of 

b will receive as great a pressure as the bottom of a. 

Again, if the vessel c, broad at the top, be narrowed to 

only an inch in diameter at bottom, the pressure upon 

that inch will still be the same, most of the weight of 

its contents resting against the sides, d d. 

If the vessel, A {Fig. 152), be filled with water to a 

height of fourteen inches, the press- 
Fig. 152. ° ' * 

==^ ure will be half a pound on every 
^^^n square inch of the bottom, or upon 

rffl|j| every square inch of the sides four- 

teen inches below the surface. If 
A | the tube, C, be an inch square, the 
| I water will be driven into it with a 
~~j3J f° rce of half a pound, and will press 
with that force against the one-inch 
surface of the stop-cock, C. If the tube, B, be now 
filled to an equal height, the same force will be exert- 
ed against the other side. To prove this, let the stop- 
cock be opened, when the two columns of water will 
remain at an exact level. 

If enough water be now poured into the tube, B, to 
fill it to the top, it will immediately settle down on a 
level with the water in A, raising the whole surface 
in the latter. This result has seemed very strange to 
many, who can not conceive how a small column of 
water can be made to balance a large one, and it has 
been therefore termed the Hydrostatic Paradox. But 
the difficulty entirely vanishes, and ceases to appear a 
paradox, when we remember that the water in the 



182 



HYDRODYNAMICS. 



larger vessel rises as much more slowly than it de- 
scends in the smaller, as the large one exceeds the 
smaller ; thus acting on the principle of virtual veloci- 
ties in precisely the same manner that a heavy weight 
on the short end of a lever is upheld by a small weight 
on the long end. The great mass of water is support- 
ed directly by the bottom of A, in the same way that 
nearly all the weight on the lever is supported by the 
fulcrum. A man who was seeking a solution to the 
absurd mechanical problem of perpetual motion, and 
who supposed that the large mass in A 
would overbalance the small column in 
B, and drive it upward, constructed a 
vessel in the form shown in Fig. 153, so 
that the small column, when forced up- 
ward, would flow back into the larger 
vessel perpetually. He was, however, 
greatlv surprised to see the fluid in both 

Attempted Perpetual ° J r 

Motion. divisions settle at the same level. 
This principle may be further explained by the fol- 
Fi g . lot. lowing experiment : A B {Fig. 154) repre- 
sents the inside of a metallic vessel, with 
a bottom, C, which slides up and down, 
water-tight. If water be poured in to fill 
the lower or larger part only, it will be 
found to press on the sliding bottom with 
a force exactly equal to its own weight ; 
that is, if there is a pound of water, it will 
press on the botton with a force equal to 
one pound. Now, if the bottom be pushed upward, so 
as to drive the water into the narrow part of the ves- 
sel, the pressure upon the bottom becomes instantly 




HYDROSTATIC BELLOWS. 



183 



much greater, or equal to many pounds, the water be- 
ing the same in quantity, but with a much higher 
head than before. Suppose the narrow part of the ves- 
sel is twenty times smaller than the larger part, then, 
in pushing the bottom up one inch, the water is driven 
twenty inches upward in the tube. So then, accord- 
ing to the rule of virtual velocities, it will require 
twenty times the force, because it moves upward twen- 
ty times faster.* This, then, is precisely similar to the 
instance where a pound on the longer end of a steel- 
yard balances twenty pounds on the shorter end. In 
this instance, the upper parts, D D, of the vessel oper- 
ate as the fulcrum of a lever, and offer resistance to the 
sliding part as soon as the water begins to ascend the 
tube. 



HYDROSTATIC BELLOWS. 

This principle is shown in the Hydrostatic Bellows 
Fig. 155. (Fig'. 155), which consists of two round 
)e pieces of board, connected by a narrow 
strip of strong leather ; into it is inserted 
a long narrow tube, B, with a small fun- 
nel, e, at the top. When water is poured 
into this tube, it will raise a weight as 
much greater than the weight of the 
water in the tube as the surface of the 
upper board exceeds the cross-section of 
the tube. Thus, if a pound of water fills 
Hydrostatic Beiiou-s. a tube half an inch in diameter, and the 
bellows is two feet in diameter, then this pound will 

* The pressure will be as great upon the bottom as if the vessel 
continued a uniform size all the way up, as shown by the dotted lines. 




184 HYDRODYNAMICS. 

raise more than two thousand pounds on the bellows 
(if it is strong enough), because the surface of the bel- 
lows is more than two thousand times greater. 

In the same way, a strong, iron-bound hogshead may 
be burst with the weight of a single gallon of water by 
pouring it into a long and narrow tube set upright 
into the bung of the hogshead. If, for instance, the 
inner surface of the hogshead be 20 square feet, or 
2880 square inches, a tube of water 23 feet high will 
press with a force of 10 pounds on every square inch, 
or equal to a force of 28,800 pounds, or 14 tons, on the 
whole surface. 

HYDROSTATIC PRESS. 

The Hydrostatic Press owes its extraordinary power 
to a similar principle ; but, instead of a bellows, there 
is a moving piston in a strong metallic cylinder ; and 
instead of being worked by the mere weight of the 
water, it is driven into the cylinder by means of the 
lever of a powerful forcing-pump. An instrument of 
this sort, possessing enormous power, was used to ele- 
vate the great tubular iron bridge in England. It was 
found necessary to make the sides of the cylinder into 
which the water was driven no less than eleven inches 
thick, of solid iron ; and so great was the pressure giv- 
en to the confined water, that it would have forced it 
up through a tube higher than the summit of Mont 
Blanc. In the port of New York, vessels of a thousand 
tons burden have been lifted by the hydrostatic press. 

This machine is applied in compressing hay, cotton, 
and other bulky substances into a compact form, so 
that they may occupy but little space for conveyance 



HYDROSTATIC PRESS. 



185 



to distant markets. The following figure {Fig. 156) 
exhibits the different parts of this powerful machine. 



Fig. 156. 




Hydrostatic Press. 

A is a cistern to supply water, which is raised by work- 
ing the handle, B, of the forcing-pump ; the water 
passes through the valve, C, opening upward, and 
through the spring valve, D, opening toward the large 
cylinder, E. Being thus driven into the space, E, it 
raises the piston, F, and exerts a prodigious pressure 
upon the mass of hay or cotton, G. The piston is low- 
ered by turning the screw, H, which allows the water 
to pass back into the cistern at I. In the figure the 
hay is shown as visible to the sight, in order to repre- 
sent the whole more plainly; but in practice it is 



186 HYDRODYNAMICS. 

thrown into a square box or chamber of strong plank, 
of the size of the intended bundle. One side is hung 
upon stout hinges, and is opened for the removal of the 
hay when the pressing is completed. 

To estimate the power of this machine, divide the 
square of the diameter of the piston, F, by the square 
of the diameter of the piston of the forcing-pump, and 
multiply the quotient by the power of the lever, B. 
For example, suppose the piston, F, is 16 inches in di- 
ameter, and the piston of the forcing-pump is 2 inches 
in diameter ; then the square of 16 is 256. Divide 
this by 4, the square of 2, and the result will be 64. 
If the lever, B, increases the power five times, the 
whole power of the machine will be 320 ; that is, a 
force of one pound applied to the lever will raise the 
large piston with a force equal to 320 pounds ; or, if a 
force of 100 pounds be given to the lever, the power 
will be 32,000 pounds, or 16 tons. Reducing the di- 
ameter of the smaller piston to half an inch, and in- 
creasing the force of the lever to twenty times, the 
whole power exerted will be thirty-two times as great, 
or equal to 960 tons. In ordinary practice, it is more 
convenient and economical to reduce the diameter of 
the larger piston to a few inches only, making the 
forcing-pump correspondingly small, the power depend- 
ing entirely on the disproportion between them. Such 
presses may be worked rapidly by horse, water, or steam 
power. 

One great advantage which the hydrostatic press 
possesses over those worked by screws results from 
the little friction among liquids, nearly the only fric- 
tion existing in the whole machine being that of the 



SPECIFIC GRAVITIES. 



187 



two pistons, which is comparatively small. Another 
is the smallness of the compass within which the whole 
is comprised ; for a man might, with one not larger 
than a tea-pot, standing before him on a table, cut 
through a thick bar of iron with as much ease as he 
could chip pasteboard with a pair of shears. 



SECTION III. 



SPECIFIC GRAVITIES. 



Fig. 157. 



In connection with Hydrostatics, the subject of the 
specific gravities of bodies is one of importance. The 
specific gravity of a substance is its comparative 
weight with some other substance, an equal bulk of 
each being taken. "Water is usually the standard for 
comparison. 

To ascertain the specific gravity, weigh the body 
both in and out of water, and observe the difference ; 
then divide the whole weight by this difference, and 
the quotient will be the specific gravity of the body. 
For example, if a stone weighs 12 
lbs. out of water and 7 lbs. in 
water, divide ,12 by 5, and the 
quotient is 2.4, which shows that 
the stone is 2^ times heavier than 
water. Figure 157 shows the 
mode of weighing the body in 
water, by suspending it beneath 
a balance on a hair or thread. 
It was in a similar way that 

Instrument J, ir taking Specific J 

Gravities. Archimedes succeeded in detect- 

ing the suspected fraud in the manufacture of the gold- 




188 HYDRODYNAMICS. 

en crown of the ancient king of Syracuse. He first 
weighed it, and then found that it displaced more wa- 
ter when plunged in a vessel just filled, than a piece of 
pure gold, and also that it displaced less than silver, 
whence he inferred the mixture of these two metals. 

When the specific gravity of a substance lighter than 
water is to be ascertained, it is loaded down by a 
weight, so as to sink in water, for which allowance is 
made in the calculation. A very simple way to deter- 
mine this in different kinds of wood is to form them 
into rods or sticks of uniform size throughout, and then 
to observe what portion of them sink when placed end- 
wise in water. 

A knowledge of the specific gravities of various sub- 
stances becomes useful in many ways, among which 
is ascertaining the weight of any structure, machine, 
or implement, according to the material used in its 
manufacture ; determining the cost, by the pound, of 
such material ; or knowing the bulk or size of any load 
for a team. The latter may often become of great use 
in ordinary practice, by enabling the teamster to cal- 
culate beforehand the amount of load to give his horses, 
whether in timber, plank, brick, lime, sand, or iron, 
without first subjecting them to overstraining exer- 
tions in consequence of error in random guessing. 

Tables of specific gravities, for this purpose, and 
weights of a cubic foot of different substances, are giv- 
en in the Appendix. 



VELOCITY OF FALLING WATER. 189 



CHAPTER II. 

HYDRAULICS. 

SECTION I. 
VELOCITY OF FALLING WATER. 

Liquids in motion are subject to the same laws as 
solids in motion. Falling water increases in velocity 
at the same rate that the motion of falling solids is ac- 
celerated, as already explained under the head of Grav- 
itation. Thus a perpendicular stream of water de- 
scends one foot in a quarter of a second, four feet in 
half a second, nine feet in three fourths of a second, 
and sixteen feet in one second. Like falling solids, 
the velocity at the end of the first quarter will be eight 
feet per second ; at the end of the second quarter, six- 
teen feet per second ; at the end of the third quarter, 
twenty-four feet per second ; and at the end of the 
fourth quarter, thirty-two feet per second. 

Now, if there be an orifice made in the side of a ves- 
sel of water, the water will spout out with the same 
swiftness as if it fell perpendicularly from an equal 
height, were it not retarded a little by friction. For 
example, if the head of water is one foot above the 
orifice, the velocity would be at the rate of eight feet 
per second, but for friction, which reduces it to about 
five and a half feet* per second. The velocity for any 
other height of head may be easily found by deduct- 
ing the same proportionate rate from the velocity of a 

Or, more accurately, 5.4 feet per second. 



190 HYDRODYNAMICS. 

falling body. Thus, for example, if the head be six- 
teen feet, the speed would be thirty-two feet (as shown 
under Gravitation), from which, deducting the fric- 
tion, the real velocity would be about twenty-two feet 
per second. 

It has been already shown that the velocity of a fall- 
ing body increases at the same rate as the increase in 
the time of falling ; for instance, the speed is twice as 
great in two seconds as in one ; three times as great in 
three seconds ; four times as great in four seconds, and 
so on. But the distance fallen through increases as 
the square of the time ; that is, it is four times as great 
in two seconds, nine times as great in three seconds, 
sixteen times as great in four seconds, &c. Thus we 
see that, in order to produce a two-fold velocity, a four- 
fold height is necessary, &c. So also in the escape of 
water under a head: to double the velocity of the 
stream, the head must be four times as high ; to triple 
it, the head must be nine times as high, &c. 

DISCHARGE OF WATER THROUGH ORIFICES AND PIPES. 

The discharge of water from a vessel is greatly in- 
fluenced by the nature of the orifice through which it 
flows. If, for example, a vessel or cistern have a thin 
bottom of tin, with a smooth circular hole, we might 
naturally suppose that the discharge would be as easy 
as it could be made, and that water would pass as rap- 
idly through it as through any orifice of an equal size. 
But this is not the fact. As the particles approach 
this orifice, their motion throws them across, and they 
partly obstruct the opening ; it will be seen that they 
converge toward a point just under the orifice, where 



DISCHARGE OF WATER THROUGH ORIFICES AND PIPES. 191 



Fig. 158. 

.^ijliiliil'il 




the stream will be considerably con- 
tracted (Fig: 158). If a short tube be 
inserted into the hole (the head being 
the same), this crossing of particles will 
be partly prevented, and the liquid will 
flow more rapidly. The greatest ef- 



Fig. 159. 



Fig. 160. 




feet is produced 
when the tube 
is twice as long 
as its diameter 
(Fig: 159). If 
the tube be en- 
larged at its 
upper and low- 
er end, similar 
to the form of the contracted 
stream of water in Fig-. 158, the quantity 
discharged is greatly increased (Fig. 160). 

When water flows down an inclined plane, the same 
law applies as to the motion of a solid body rolling down 
a plane. The velocity increases as the square of the dis- 
tance, and is the same as the velocity of a body falling 
freely downward from a height equal to the perpendic- 
ular height of the plane. Unless the stream, however, is 
very large, its speed is quickly diminished by the friction 
of its channel,* until this friction becomes as great as 
the descending force, after which the motion becomes 
uniform. Hence the reason that large streams, with an 
equal degree of descent, flow so much more rapidly than 
small ones, the gravitating force being so much great- 
er that friction has a less retarding effect upon them. 

* Which increases as the square of the velocity. 



192 HYDRODYNAMICS. 

In pipes which wholly surround the flowing stream, 
the friction becomes still greater, and the difficulty is 
only obviated by making the pipe of larger dimensions 
than would otherwise be necessary, so as to allow a free 
passage of a sufficient quantity of water through the 
centre of the tube, while a ring or hollow cylinder of 
water is nearly at rest all around it. The tables in 
the Appendix exhibit this decreased velocity in tubes 
of various sizes. 



SECTION III. 
VELOCITY OF WATER IN DITCHES. 

It is often of great practical utility to know what 
amount of water may be carried off in draining or sup- 
plied in irrigation by channels of any given size and 
descent. The following rule will apply to all cases, 
from the plow-furrow to the mill-race, or even to the 
large river, and may be used by any boy who under- 
stands common arithmetic, and which is illustrated 
and made plain by the example that follows the rule. 

To ascertain the mean (or average) velocity of wa- 
ter in a straight channel of equal size throughout : 

Let /= the fall in two miles in inches; 

Let d^the hydraulic mean depth; 

Let v=the velocity in inches per second; 
then the rule is thus expressed, v = 0.91\S fd, or, in 
plain words, the velocity is equal to the hydraulic mean 
depth multiplied by the fall, with the square root of 
this product extracted, and then multiplied by 0.91. 

The "hydraulic mean depth" is found by dividing 
the cross-section of the channel by the perimeter or 



VELOCITY OF WATER IN DITCHES. 193 

border. The perimeter is the aggregate breadths of 
the sides and bottom of the channel. 

The rule will be rendered quite plain by an exam- 
ple. Suppose a smooth furrow is cut six inches wide 
and four inches deep, with perpendicular sides, and 
that it descends one inch in a rod ; to find the quanti- 
ty of water that will flow through it. One inch fall in a 
rod is 320 inches in a mile, or 640 in two miles. The 
perimeter in contact with the water will be six inches 
on the bottom, and four inches in each side = 14 inches. 
The area of the cross-section will be 6 times 4 = 24, which 
divided by 14, the perimeter, gives 1.7= the hydraulic 
mean depth. Then, by applying the preceding rule : 

^=0.91^640x1.7, or ?; = 0.91 x 33=30 inches, 
the velocity per second, which would be about three 
gallons per second, or three hogsheads per minute. 

An open ditch, therefore, with smooth sides, convey- 
ing a stream of this size, would carry off in one hour, 
from an acre of land, all the water which might fall 
by half an inch of rain during the wet season ; for half 
an inch of rain would be 180 hogsheads per acre, which 
would pass off in one hour ; or it would supply in one 
hour, by the process of irrigation, as much water as a 
heavy shower of half an inch. Where the descent is 
greater, the increased quantity may be readily calcu- 
lated by the rule given. The capacity of smooth-sided 
underground channels may be determined in the same 
way; but if built of rough stones, great allowance 
must be made, as they will retard the flow of water. 

In common practice, too, even with straight, open 
ditches, the velocity will be much diminished by the 
rough sides. 

I 



194 



HYDRODYNAMICS. 



LEVELING INSTRUMENTS. 

The simplest mode of leveling, or ascertaining the 
slope for ditches, is to cut a few* yards of the ditch so 
that water may stand in it, and then to set two sticks 
perpendicularly, both rising to an equal height above 
the surface. The sticks should he measured at equal 
distances from the top downward and marked, and 

Fig. 161. 




Fig. 162. 

I'i ' i'i'i'i.'i'i 1 



Simple method of taking levels. 

then pressed into the earth till the water reaches the 
mark. The level may then be determined with much 
accuracy by "sighting" over the tops of these sticks. 

Figure 161 exhibits this 
TTpT 1 arrangement. The shorter 
the sticks, and the longer 
the piece of water, the less 
will be the liability to error. 
The following simple 
mode may be sufficiently 
accurate where the descent 
of the ditch is considerable. 
A {Fig. 162) is a common 
square, placed in a slit in 
the top of the stake, B. By 
means of a plumb-line, the 
square is brought to a level, 
when a thumb-screw at C 
fixes it fast. If the square 



Simple Leveling Instrument. 



LEVELING INSTRUMENTS. 



195 



is two feet long, and is so carefully adjusted by means 
of the plumb-line as not to vary more than the twen- 
tieth of an inch from a true level, which is easily ac- 
complished, then a twentieth of an inch in two feet 
will be one inch in forty feet, a sufficient degree of ac- 
curacy for many cases. 

Where greater accuracy is required, as in long and 
nearly level ditches, the "water level" may be used. 
Fig. 163. It may be made of a 

^Ulead tube about three 
b feet long, bent up an 
/=£, inch or two at each end, 

and stiffened by fasten- 
ing to a wooden bar, 
A, B (Fig-. 163). Into 
each end is cemented, 
with sealing-wax, a 
small and thin phial 
with the bottom broken 
off, so that when the tube is filled with water it may 
rise freely into the phials. If the tube be now filled 
with water colored with .cochineal or any dye-stuff, and 
then placed upon the tripod, C, by looking across the 
two surfaces of liquid in the phials, an accurate level 
may be obtained. "When not in use, a cork is placed 
Fig-164. into each phial. " Sights" of equal height, fast- 
ened to pieces of cork floating on the water, as 
shown in Fig-. 164, give a more distinct line for 
the eye. The sights are formed of fine threads 
or hairs stretched across the square openings. 
To ascertain whether these threads are both of 
equal heights above the water, let a mark be made 




Common Leveling- Instrument. 



196 HYDRODYNAMICS. 

where they intersect some distant object ; then reverse 
the instrument, or turn it end for end, and observe 
whether the threads cross the same mark. If they do, 
the instrument is correct ; but if they do not, then one 
of the sights must be raised or lowered until it be- 
comes so. 

In laying out canals and rail-roads, where extreme 
accuracy is needed, the spirit-level attached to a tele- 
scope is used. So great is the perfection of this instru- 
ment, that separate lines of levels have been run with 
it for sixty miles without varying two thirds of an inch 
for the whole distance. 

The use of a cheap and simple instrument to determ- 
ine the position and descent of ditches with ease and 
precision, before commencing with the spade, will save 
a vast amount of the trouble and expense which those 
often meet with whose only method is to " cut and try}'' 



SECTION III. 
HYDRAULIC MACHINES. 

ARCHIMEDEAN SCREW. 

Machines for raising water are of frequent use on 
every farm. One of the simplest contrivances for this 
purpose is the Screw of Archimedes. It may be easily 
made by winding a lead tube around a wooden cylin- 
der or rod (Fig. 165), in the form of a screw. "When 
placed in an inclined position, with one end in water, 
and made to revolve, the water resting at the lower side 
of each turn of the screw is gradually carried from one 
end to the other, and discharged at the upper extremi- 



ARCHIMEDEAN ROOT-WASHER. 

Fig. 165. 



197 




The Screw of Archimedes 



ty. Its simplicity and small liability to get out of 
order renders the Archimedean Screw sometimes use- 
ful where water is to be raised from an open stream to 
a short distance, as for irrigation, the motion being 
easily imparted to it by means of a small water-wheel 
driven by the stream. 

ARCHIMEDEAN ROOT-WASHER. 

This principle has been successfully applied in the 
Archimedean Root-washer (Fig. 166). The roots to 




Croskill's Archimedean Root-washer. 



be washed are first delivered into a hopper, from which 



198 HYDRODYNAMICS. 

they pass into an inclined cylinder made of strips of 
wood with grate-like openings. The cylinder has two 
portions separated by a partition, in the first of which 
they remain while the handle is turned for washing 
them. As soon as the washing is finished, the motion 
of the handle is reversed, which throws them into the 
other part, which has a spiral partition, along which 
they pass till they drop into a spout outside. 

The same principle is adopted in the horizontal corn- 
sheller, shown by the annexed figure {Fig. 167), al- 



Fig. 167. 




though this machine has no connection with hydraul- 
ics. The corn in the ear is thrown into the hopper at 
one end, and is quickly separated from the cob by rows 
of teeth revolving in a concave bed and set spirally, 
which, by this arrangement, carry along the cobs and 
eject them from the other end. This is a good corn- 
shelling machine for horse-power. 

The sausage-mincing machine operates on a similar 
principle. 

PUMPS. 

Great improvement has been made in the common 
pump for farms within the past ten years. The best 
cast-iron pumps, made almost wholly of this metal, far 



PUMPS. 



199 



rig- 168. exceed in durability and ease of 

working those formerly con- 
structed of wood, and excel all 
others in cheapness. Fig. 168 
exhibits the working of the com- 
mon pump, the water first pass- 
ing through the fixed valve be- 
low, and then through the one 
in the piston ; both opening up- 
ward, it can not flow back with- 
out instantly shutting them. 
The water is driven up by the 
pressure of the atmosphere, ex- 
plained in the next chapter. 

The most perfect pump, per- 
haps, in present use, 
is the best-construct- 
ed Chain Pump, a 
cross-section of one 
of which is here 
shown (Fig. 169). 
The chain is made 
to revolve rapidly on the angular wheel by 
means of a winch attached to the upper one, 
and being furnished with a regular succes- 
sion of metallic discs which nearly fit the 
bore in the tube, «, the water is carried up 
in large quantities. "When the motion is 
discontinued, the water settles down again 
into the well, and consequently this pump is 
not liable to accident by freezing. By 
sweeping rapidly through the water, it pre- Chain Pum P- 




Fig. 169. 



Common Pump : b, lower or fixed 
valve , G, piston with valve, a, 
opening upward; D d, piston- 
rod ; F, spout. 



200 HYDRODYNAMICS. 

serves it in better condition, and prevents stagnation. 
The friction being very small, it will last a long time 
without wearing out. 

THE WATER-RAM. 

One of the most ingenious and useful machines for 
elevating water is the Water-ram. It might be em- 
ployed with great advantage on many farms, were its 
principle and mode of action more generally understood. 
By means of a small stream, with only a few feet fall, 
a current of water may be driven to an elevation of 
fifty to a hundred feet above, and conveyed on a higher 
level to pasture-fields for irrigation, or to cattle-yards 
for supplying drink to domestic animals, or to the kitch- 
en of dwellings for culinary purposes. 

Its power depends on the momentum of the 

Fig 170. stream. Its principal 

| parts are the reservoir 

J, ■/* *\ or air-chamber, A {Fig. 

if a J 170), the supply-pipe, 

\^=ets B, and the discharge 

N. \V V =F{ pipe, C. The running 

>^S. ^> ^-,V^ JlDl stream rushes down 

^Sr-w — - — est-^ tlie supply -pipe, B > 
water-ram. and, striking the waste 

valve, D, closes it. The stream being thus suddenly 
stopped, its momentum opens the valve, E, upward, 
and drives the water into the reservoir, A, until the 
air within, being compressed into a smaller space, 
by its elasticity bears down upon the water, and again 
closes the valve, E. The water in the supply-pipe, B, 
has by this time expended its momentum and stopped 



THE WATER-RAM. 201 

running ; therefore the valve, D, drops open again, and 
permits it to escape. It recommences running, until 
its force again closes the waste valve, D, and a second 
portion of water is driven into the reservoir as before, 
and so it repeatedly continues. The great force of the 
compressed air in the reservoir drives the water up the 
discharge-pipe, C, to any required height or distance. 

The mere iveight of the water will only cause it to 
rise as high as the fountain-head; but like the mo- 
mentum of a hammer, which drives a nail into a solid 
beam, which a hundred pounds would not do by press- 
ure, the striking force of the stream exerts great 
power. 

The discharge-pipe, C, is usually half an inch in di- 
ameter, and the supply-pipe should not be less than an 
inch. A fall of two or three feet in the stream, with 
not less than half a gallon of water per minute, with 
a supply-pipe forty feet long, will elevate water to a 
height as great as the strength of common half-inch 
lead pipe will bear.* The greater the height in pro- 
portion to the fall of the stream, the less will be the 
quantity of water elevated as compared with the quan- 
tity flowing in the stream. 

Unlike a pump, there is no friction or rubbing of 
parts in the water-ram, and it will act for years with- 
out repairs, continuing through day and night its 

* When water is raised to a considerable elevation by means of the 
water-ram, the reservoir must possess great strength. If the height 
be one hundred feet, the pressure, as shown on a former page, is about 
forty-four pounds to the square inch. With an internal surface, there- 
fore, of only two square feet, the force exerted by the column of water, 
tending to burst the reservoir, would be equal to more than twelve 
thousand pounds. 

12 



202 



HYDRODYNAMICS. 



constant and regular pulsations, unaltered and unob- 
served. 



WATER-ENGINES, 

including those for extinguishing fires and for irriga- 
ting gardens, are constructed on a principle quite sim- 
ilar to that of the water-ram. Instead, however, of 
compressing the air, as in the ram, by the successive 
strokes of a column of running water, it is accom- 
plished by means of a forcing-pump, driving the water 
into the reservoir, from which it is again expelled with 
great power by means of the elasticity of the com- 
pressed air. Fig. Ill represents a garden-engine, 




Garden-enshie. 



movable on wheels, which may be used for watering 
gardens, washing windows, or as a small fire-engine. 
Fig. 172 (at the head of the opposite page) is another 
of smaller size, for the same purpose, and in a very 
neat and compact form, the working part being within 
the cylindrical case. 



THE FLASH- WHEEL. 
Fig. 172. 



203 




Cylindrical Garden-engine. 



THE FLASH-WHEEL 

is employed with great advantage where the quantity 
of water is large and is to be raised to a small height. 
It is like an undershot- wheel with its motion reversed 
(Fig: 173, p. 204), where the arrows show the direc- 
tion of the current when driven upward. It must, of 
course, be made to fit the channel closely, without 
touching and causing friction. In its best form its 
paddles incline backward, so as to be nearly upright at 
the time the water is discharged from them into the 
upper channel. It has been much used in Holland, 
where it is driven by wind-mills, for draining the sur- 
face-water off from embanked meadows. In England 



204 



HYDRODYNAMICS. 
Fig. 173.- 




Flash or fen wheel for raising water rapidly short distances. 

it has been driven by steam-engines ; and in one in- 
stance, an eighty-horse-power engine, with ten bushels 
of coal, raised 9840 tons of water six feet and seven 
inches high in an hour. This is equal to more than 
29,000 lbs. raised one foot per minute by each horse- 
power, showing that very little force is lost by friction 
in the use of the flash- wheel. 



Fig. 174. 




SECTION IV. 
WAVES. 

NATURE OF WAVES. 

An inverted syphon, or bent tube like 
that shown in Fig: 174, may be used 
to exhibit the principle on which de- 
pends the motion of the waves of the 
sea. The action of the waves on shores 



THE WATER NOT PROGRESSIVE. 205 

and tanks, and the inroads which they make upon 
farms situated on the borders of lakes and large rivers, 
present an interesting subject of inquiry. 

If the bent tube {Fig. 174) be nearly filled with wa- 
ter, and the surface be driven down in one branch by 
blowing suddenly into it, the liquid will rise in the 
other branch. The increased weight or head of this 
raised column will cause it to fall again, its moment- 
um carrying it down below a level, and driving the 
water up the other branch. The surfaces will, there- 
fore, continue to vibrate until the force is spent. The 
rising and falling of waves depend on a similar action. 
The wind, by blowing strongly on a portion of the wa- 
ter of the lake or sea, causes a depression, and produces 
a corresponding rise on the adjacent surface. The 
raised portion then falls by its weight, with the added 
force of the wind upon it, until the vibrations increase 
into large waves. 

THE WATER NOT PROGRESSIVE. 

The waves thus produced have a progressive motion 
(for reasons to be presently shown), as every one has 
observed. A curious optical deception attending this 
advancing motion has induced many to believe that 
the water itself is rolling onward ; but this is not the 
fact. The boat which floats upon the waves is not 
carried forward with them ; they pass underneath, now 
lifting it on their summits, and now letting it sink into 
the hollows between. The same effect may be observ- 
ed with the water-fowl, which sits upon the surface. 
It often happens, indeed, that the waves on a river roll 
in an opposite direction to the current itself. 



206 HYDRODYNAMICS. 

If a cloth be laid over a number of parallel rollers 
so far apart as to allow the cloth to fall between them, 
and a progressive motion be then given to them, the 
cloth remaining stationary, a good representation of 
waves will be afforded, and the cloth will appear to ad- 
vance ; or if a strip of cloth be laid on a floor, repeated 
jerks at one end will produce a similar illusion. 

It is only the form of the wave, and not the water 
which composes it, which has an onward motion. Let 
the dark line in Fig-. 175 represent the surface of the 

Fig. 175. 




water. A is the crest of one of the waves, and being 
higher than the surface at B, it has a tendency to fall, 
and B to rise. But the momentum thus acquired car- 
ries these points so far that they interchange levels. 
The same change takes place with the other waves, 
and the dotted line shows the newly-formed surface as 
the water thus sinks in one place and rises in another. 
The same process is again repeated, and each wave 
thus advances further on, and the progressive motion 
is continually kept up. 

BREADTH AND VELOCITY OF WAVES. 

Each wave contains at any one moment particles 
in all possible stages of their oscillation ; some rising 
and some falling ; some at the top and some at the bot- 
tom ; and the distance from any row of particles to the 
next row that is in precisely the same stage of oscilla- 



BREADTH AND VELOCITY OF WAVES. 207 

tion, is called breadth of the wave, that is, the distance 
from crest to crest or from hollow to hollow. 

There is a striking similarity between the rising and 
falling of waves and the vibrations of a pendulum, and 
it is a very interesting and remarkable fact that a wave 
always travels its own breadth in precisely the same 
time that a pendulum whose length is equal to that 
breadth performs one vibration. Thus, a pendulum 
39 1 inches long beats once in each second, and a wave 
whose breadth is 39 £ inches travels that breadth in 
one second. The length of a pendulum must be in- 
creased as the square of the time for its vibrations ; 
that is, to beat but once in two seconds, it must be 
four times as long as for one second ; to beat once in 
three seconds, it must be nine times as long, and so on. 
In the same way, waves which travel their breadth in 
two seconds are four times as wide as those traveling 
their breadth in one second ; and thus their breadth, 
and consequently their speed, increases as the square 
of the time. Large waves, therefore, roll onward with 
far greater velocity than small ones. If only thirty- 
nine inches wide, they move about two and a quarter 
miles an hour, and pass once each second ; if 

13 feet wide, they move 4£ miles an hour, passing once in 2 seconds. 

52 do. do. 9 do. do. 4 do. 

209 do. do. 18 do. do. 8 do. 

836 do. do. 36 do. do. 16 c!o. 

Although the water itself does not advance where 
there is much depth, yet when it reaches a shore or 
beach, the hard and shallow bottom prevents it from 
falling or subsiding, and it then rolls onward with a 
real progressive motion by the momentum it has ac- 



208 HYDRODYNAMICS. 

quired, and breaks into foam and lashes the earth and 
rocks. The sea-billows are sometimes twenty-five feet 
in elevation,* and when these advance upon a stranded 
ship on a lee shore, with the speed of a locomotive, 
their effects are in the highest degree appalling, and 
iron bolts are snapped and massive timbers crushed 
beneath their violence. 

PREVENTING THE INROAD OF WAVES. 

To prevent the inroads of lake waves upon land, the 
remedies must vary with circumstances. The diffi- 
culty would be small if the water always stood at the 
same height. The greatest mischief is usually done 
when they rise over the beach of sand and gravel which 
they have beaten for centuries. "Wooden bulwarks soon 
decay. Where loose stone can be had in large quan- 
tities they may be cheapest, but they are not unfre- 
quently placed too near low- water mark to protect the 
banks. Substances which offer a gradual impediment 
to the waves are often quite effectual, though not for- 
midable in themselves. It is curious to observe how 
so slender a plant as the bulrush, growing in water 
several feet deep, will destroy the force of waves. If 
it grew only near the shore, where the water has pro- 
gressive motion, it would soon be dashed in heaps on 
the beach. Parallel hedgerows of the osier willow, 
protected by a wooden barrier until well grown and 
established, would in many cases prove efficient. 

Stones and timber bulwarks are often made need- 
lessly liable to injury by being built nearly perpen- 

* No authentic measurement gives the perpendicular height of 
waves more than twenty-five feet. 




PREVENTING THE INROAD OP WAVES. 209 

dicular, and the waves break suddenly and with full 
Fig. 176. force, like the blows 

of a sledge against 
them. A better form 
^ is shown in Fig: 
176, where a slope 
is first presented to weaken their force without impos- 
ing a full resistance, and their strength is gradually 
spent as they rise in a curve. A more gradual slope 
than the figure represents would be still better. It is 
on this principle that the stability of the world-renown- 
ed Eddystone light-house depends. The base spreads 
out in every direction, like the trunk of a tree at the 
roots; and although the spray is sometimes dashed 
over its lofty summit by the violence of the storm, it 
has stood unshaken on its rocky base far out in the sea, 
against the billows and tempests, for nearly a century. 
An instance occurred many years ago in England, 
where the superiority of knowledge over power and 
capital without it was strongly exemplified. The sea 
was making enormous breaches on the Norfolk and 
Suffolk coast, and inundated thousands of acres. The 
government commissioners endeavored to keep it out 
by strong walls of masonry and breakwaters of timber, 
built at great expense ; but they were swept away by 
the fury of the billows as fast as they were erected. 
A skillful engineer visited the place, and with much 
difficulty persuaded them to adopt his simple plan. 
Observing the slope of the beach on a neighboring 
shore, he directed that successive rows of fagots or 
brush be deposited for retaining the sand, which was 
carted from the hills, forming an embankment with a 



210 HYDRODYNAMICS. 

slope similar to that of the natural beach. Up this 
slope the waves rolled, and became gradually spent as 
they ascended, till they entirely died away. The 
breach was effectually stopped, and this simple struc- 
ture has ever since resisted the most violent storms of 
the Grerman Ocean. 



SECTION V. 
CONTENTS OF CISTERNS. 



Connected with the subject of hydraulics is the 
collection and security of water falling upon roofs, in 
all cases where a deficiency is felt by farmers in the 
drought of summer. The amount which falls upon 
most farm-buildings is sufficient to furnish a plentiful 
supply to all the domestic animals of the farm when 
other supplies fail, if cisterns large enough to hold it 
were only provided. Generally speaking, none at all 
are connected with barns and out-buildings, and even 
when they are furnished, they are usually so small as 
to allow four fifths of the water to waste. 

If all the rain that descends in the Northern States 
of the Union should remain upon the surface without 
sinking in or running off, it would form each year a 
depth of about three feet. Every inch that falls upon 
a roof yields two barrels for each space ten feet square, 
and seventy-two barrels a year are yielded by three 
feet of rain. A barn thirty by forty feet supplies annu- 
ally from its roof 864 barrels, or enough for more than 
two barrels a day for every day in the year. Many 
farmers have in all five times this amount of roof, or 
enough for twelve barrels a day yearly. If, however, 



RULE FOR DETERMINING THE CONTENTS. 



211 



this water was collected, and kept for the dry season 
only, twenty or thirty barrels daily might he used. 

In order to prevent a waste of water on the one hand, 
and to avoid the unnecessary expense of too large cis- 
terns, their contents should he determined beforehand 
by calculation. 



RULE FOR DETERMINING THE CONTENTS. 

A simple rule to determine the contents of a cistern, 
circular in form, and of equal size at top and bottom, 
is the following : Find the depth and diameter in 
inches ; square the diameter, and multiply the square 
by the decimal .0034, which will find the quantity in 
gallons* for one inch in depth. Multiply this by the 
depth, and divide by 31^, and the result will be the 
number of barrels the cistern will hold. 

For each foot in depth, the number of barrels an- 
swering to the different diameters are, 

For 5 feet diameter 4.66 barrels. 



6.71 

9.13 

11.93 

15.10 



10 " ....... 18.65 

By the rule above given, the contents of barn-yard 
cisterns and manure tanks may be easily calculated 
for any size whatever. 

* This is the standard gallon of 231 cubic inches. The gallon of 
the State of New York contains 221.184 cubic inches, or 6 pounds at 
its maximum density. 



212 HYDRODYNAMICS. 

DETERMINING THEIR SIZE. 

The size of cisterns should vary according to their 
intended use. If they are to furnish a daily supply 
of water, they need not he so large as for keeping sup- 
plies for summer only. The average depth of rain 
which falls in this latitude, although varying consid- 
erably with season and locality, rarely exceeds seven 
inches for two months. The size of the cistern, there- 
fore, in daily use, need never exceed that of a body of 
water on the whole roof of the building seven inches 
deep. To ascertain the amount of this, multiply the 
length by the breadth of the building, reduce this to 
inches, and divide the product by 231, and the quotient 
will be gallons for each inch of depth. Multiplying by 
7 will give the full amount for two months' rain fall- 
ing upon the roof. Divide by 31^, the quotient will 
be barrels. This will be about fourteen barrels for 
every surface of roof ten feet square when measured 
horizontally. Therefore, a cistern for a barn 30 by 40 
feet should hold 168 barrels ; that is, as large as one 
ten feet in diameter and nine feet deep. Such a cis- 
tern would supply, with only thirty inches of rain year- 
ly, no less than 630 barrels, or nearly two a day. 

Cisterns intended only for drawing from in times of 
drought, to hold all the water that may fall, should bo 
about three times the preceding capacity. 



PART III, 

PNEUMATICS. 



CHAPTER I. 



PRESSURE OF AIR. 



Fig. 177 



Pneumatics treats of the mechanical properties of 
the air. 

The actual weight of the 
air may be correctly found by 
weighing a strong glass ves- 
sel furnished with a stop-cock, 
a [Figure 177), after the air 
has been withdrawn from it by 
means of an air-pump. Let 
it be accurately balanced by 
weights in the opposite scale ; 
then turn the stop-cock and ad- 
mit the air, and it will imme- 
diately descend, as shown in 
the figure. The weight of the 
admitted air may be ascertain- 
ed by adding weights till it is 
again balanced. 




Balance for Weighing Air. 



HEIGHT AND WEIGHT OF THE ATMOSPHERE. 

The atmosphere which covers the earth extends up- 
ward to a height of about fifty or sixty miles. At the 



214 PNEUMATICS. 

surface of the earth the air is about eight hundred times 
lighter than the water, and the higher we ascend, the 
rarer or lighter it becomes, from the diminished press- 
ure of its weight above. At seven miles high, it is 
four times lighter than at the surface ; at twenty-one 
miles, it is sixty-four times lighter ; and at fifty miles, 
about twenty thousand times lighter. At this height 
it ceases to refract the rays of the sun so as to render 
it visible at the earth's surface ; but if it decreases at 
the same rate upward, at a hundred miles high it must 
be nearly a thousand million times rarer than at the 
earth. 

If the atmosphere were uniformly of the same dens- 
ity, with its present weight, it would reach only five 
miles high. Although so much lighter than water, 
yet, from its great height, it presses upon the surface 
of the earth as heavily as a depth of thirty -three feet 
of water. This is nearly equal to fifteen pounds on 
every square inch, or more than two thousand pounds 
to the square foot. This enormous weight would in- 
stantly crush us, did not air, like liquids, press in every 
direction, so that the upward exactly counterbalances 
the downward pressure, and the air within the body 
counteracts that without. 

The weight of the atmosphere is strikingly shown 
by means of an air-pump, which pumps the air from a 
glass vessel, placed mouth downward upon the brass 
plate of the machine (Fig'. 178). "When the air is 
pumped out, and the upward or counterbalancing air 
removed, so heavy is the load upon the glass vessel, 
that a strong man could scarcely remove it from the 
plate, although it be no larger than a small tumbler. 



HEIGHT AND WEIGHT OF THE ATMOSPHERE. 215 




Air-pump. 

pressure that it can not be removed 



A glass jar with a 
mouth six inches 
across would need 
a force equal to 
nearly four hund- 
red pounds to dis- 
place it. If there 
be a glass vessel 
open at both ends, 
the hand placed on 
the top may be so 
firmly held by the 

Fig. 179. 




The Hand fastened 
by Air. 



until the air is again admitted below 
(Fig. 179). If a thin plate of glass 
be placed on the top of this open ves- 
sel, on pumping out the air, the 
weight will suddenly crush it with a 
noise like the report of a gun. 

Some interesting instances occur in nature of the 
use of atmospheric pressure. Flies walk on glass by 
means of the pressure against the outside of their feet, 
the air having been forced out beneath. In a similar 
way, some kinds of fishes cling to the sides of rocks 
under water, so as not to be swept off by the current. 
Dr. Shaw threw a fish of this kind into a pail of water, 
and it fixed itself so firmly to the bottom, that, by tak- 
ing hold of the tail, he lifted up the pail, water and all. 

It is the pressure of the atmosphere upon water that 
drives it up the barrel of a pump as soon as the air is 
pumped out from the inside. Hence the reason that 
pumps can never be made to draw water more than 



216 



PNEUMATICS. 



thirty-three feet below the piston, a height correspond- 
ing to the weight of the atmosphere. 



THE BAROMETER. 

On the same principle the Barometer is made. It 
consists of a glass tube, nearly three feet long, open at 
one end, and which is first filled with mercury, a liquid 
nearly fourteen times heavier than water. The open 
end is then placed downward in a cup of mercury. 
The weight of the mercury in the tube causes it to de- 
Fig. 180. scend until the pressure of the atmosphere on 
the mercury in the cup preserves an equilibrium, 
which takes place when the column in the tube 
has fallen to about two feet and a half high, the 
upper part of the tube being left a perfect vac- 
uum, as no air can enter (Fig: 180). Now, as 
the height of the column of mercury depends 
alone upon the weight of the atmosphere, then, 
whenever the air becomes lighter or heavier, as 
it constantly does during the changes of the 
weather, the rising or falling of the column indicates 
these changes ; and, what is very important, it shows 
the approaching changes of the weather several hours 
before they actually take place. Hence it becomes a 
valuable assistant in foretelling the weather. "When 
the mercury falls, showing that the atmosphere is be- 
coming lighter, it indicates the approach of storms or 
rain ; when it rises, a settled or fair sky follows. These 
are often foreshown before there is any change in the 
appearance of the sky. For this reason the barometer 
is sometimes called a weather-glass. It is of the 
greatest value to navigators at sea. Long voyages 




THE BAROMETER. 217 

which formerly required a year have been made in 
eight months by means of the assistance afforded by 
the barometer, admitting a full spread of canvas by 
night as well as by day, from the certainty of its pre- 
dictions. On land its indications are not so certain, and 
at some places less so than at others. Sometimes, and 
more commonly during autumn and winter, the sink- 
ing of the mercury is followed only by wind instead 
of rain. There is, however, no doubt that its use would 
be of much advantage in large farming establishments, 
more especially during the precarious seasons of haying 
and harvesting. 

The barometer is an instrument of great value in 
determining with little labor, and with considerable ac- 
curacy, the heights of mountains, hills, and the leading 
points of an extensive district of country. In rising 
above the level of the sea, the weight of the air above 
us becomes less ; that is, the pressure of the air upon 
the barometer decreases, and the column of mercury 
gradually falls as we ascend. To determine, therefore, 
the height of a mountain, we have only to place one 
barometer at its foot while another stands at the top, 
and then, by observing the difference in the height of 
the mercury, we are enabled to calculate the height of 
the mountain. The following table shows how much 
the barometer falls at different altitudes, thirty inches 
being taken for the sea-level :* 

* The mercury rarely stands as high as 30 inches at the level of the 
sea, the mean height being about 29.5 inches. But this does not af- 
fect the measurement of heights, which is determined, not by the actual 
height, but by the difference in heights. 

K 



218 



PNEUMATICS. 



At 1000 feet above the sea, the column falls to 28.91 inches. 



2000 
3000 
4000 
5000 

1 mile 

2 " 

3 " 

4 " 

5 " 
10 " 
15 " 
20 " 



27.86 

26.85 

25.87 

24.93 

24.67 

20.29 

16.68 

13.72 

11.28 

4.24 

1.60 

0.95 



At the level of the sea, the barometer falls about 
one hundredth of an inch for a rise of nine feet, or a 
little more than the tenth of an inch for a rise of one 
hundred feet. At a height of one mile it requires about 
eleven feet rise to sink the mercury a hundredth of an 
inch. 

In selecting land in mountainous districts of the 
country, where degrees of frost increase with increased 
altitudes, and where the height of one portion above 
another has an important relation to the cost of draw- 
ing loads up and down hill, the barometer might be- 
come of much practical value. 

THE SYPHON. 

The syphon operates on a principle quite similar to 
that of the pump ; but, instead of pumping out the air 
of the tube through which the water rises, a vacuum 
is created by the weight of a column of water, in the 
following way : Fig. 181 represents a syphon, which is 
nothing more than a tube bent in the form of a letter 
U inverted. Now, if this be filled throughout with 



THE SYPHON. 



219 



11 ;i water, and then placed with the short- 

er arm in the vessel of water, A, the 
weight of the column of water in the 
longer arm, which is outside, will over- 
balance the weight of the other col- 
umn, and will therefore run out in a 
stream. This tends to cause a vacu- 
um in the tube, which is instantly fill- 
ed by the water rushing up the short- 
er arm, being driven up by the pressure of the atmos- 
phere. A stream will consequently continue running 
through the syphon until the vessel is drained. 

The syphon may sometimes be very usefully em- 
ployed in emptying pools or ponds of water on high 
ground, without the trouble of cutting a ditch for this 
purpose. For instance, let a (Fig. 182) represent a 

Fig. 182. 





body of water which it is desirable to drain off; by 
placing the lead tube, b c, so that the arm, c, may be 
lowest, and applying a pump at this arm fo withdraw 
the air and fill the syphon with water, it will com- 
mence running, and continue till the water has all been 
drawn off. Difficulties, however, sometimes occur. If 
the tube is small and very long, and the descent is 
trifling, the friction of the water in the tube may pre- 
vent success. Water usually gives out small quanti- 
ties of air, which collects in the higher part of the sy- 



220 PNEUMATICS. 

phon, and after a while fills it, causing the stream to 
cease running ; but syphons for this purpose, when only ' 
a few rods in length, with several feet descent, are 
usually found to succeed well. If the discharging 
orifice is several times smaller than the tube, it is fre- 
quently of material use, by causing a slow and steady 
current through the syphon. 



WINDS. 



221 



CHAPTER II. 

MOTION OF AIR. 
SECTION I. 

WINDS. 

Wind is air in motion. Its force depends on its 
speed. When its motion is slow, it constitutes the 
soft, gentle breeze. As the velocity increases, the force 
becomes greater, and the strong gale sweeps round the 
arms of the wind-mill with the strength of many horses, 
and huge ships are driven swiftly through the waves 
by its pressure. By a still greater velocity of the air, 
its power becomes more irresistible, and solid buildings 
totter, and forest trees are torn up by the roots in the 
track of the tornado. 

The force of wind increases directly as the square 
of the velocity. Thus a wind blowing ten miles an 
hour exerts a pressure four times as great as at five 
miles an hour, and twenty-five times as great as at two 
miles an hour. The following table exhibits the force 
of wind at different degrees of velocity : 

Description. 
Hardly perceptible. 

Just perceptible. 
Light breeze. 
Gentle, pleasant wind. 



Miles an 
hour. 

1 


Pressure in lbs. on 
a square foot. 

.005 


2 


.020 i 
.045) 


3 


4 


.080} 
.125) 


5 


6 


.180i 
.320) 


r 



222 PNEUMATICS. 

Miles an Pressure in lbs. on r» m — 1-«»- 

hour. a square foot. Description. 



Pleasant, brisk wind. 
Very brisk. 
Strong, high wind. 
Very high. 



10 .500 i 

15 1.125 $ 

20 2.000 > 

25 3.125 5 

30 4.500 i 

35 6.125 5 

40 8.000 > 

45 10.125 5 

50 12.500 Storm or tempest. 

60 18.000 Great storm. 

80 32.000 Hurricane. 

100 50.000 Tornado, tearing up trees, and sweeping off 

buildings. 

These forces may "be observed at a time when the air 
is still, by a forward motion equal to that of the wind. 
Thus walking moderately gives the faint breeze against 
the face ; riding in a wagon at six miles an hour causes 
the sensation of a pleasant wind ; the deck of a steam- 
boat at fifteen miles produces a brisk blow ; while an 
open rail-car at forty miles an hour occasions a sweep 
of the air nearly resembling a tempest. 

The preceding table will enable any one to calculate 
with considerable accuracy the amount of draught 
which a horse must constantly overcome in traveling 
with a covered carriage against the wind, adding, of 
course, the speed of the horse to that of the wind. For 
example, suppose a horse with a covered carriage is 
driven against what we term " a very brisk wind," 
blowing 24 miles an hour, and pressing 3 lbs. on the 
square foot. The carriage top offers a resisting surface 
four feet square, or with sixteen square feet. Three 
times sixteen, or 48 lbs., are consequently required to 
be overcome with every onward step of the horse. 



WIND-MILLS. 223 

Now we have already seen, when treating of " appli- 
cation of labor," that a horse traveling three miles an 
hour for eight hours, will overcome only 83 lbs. with 
ordinary working, which is not double the resistance 
of the wind. Hence we perceive that more than half 
the horse's strength is lost by driving against such a 
current. At six miles an hour, all his strength, with- 
out over-driving, would be expended in overcoming 
the force of the wind, and the power required for mov- 
ing the carriage would be so much excessive labor. 
For simplifying the operation, the increased motion of 
the wind occasioned by driving against it has not been 
taken into account. 

Even with a small pressure, the loss in power is con- 
siderable for an entire day. When, for example, the 
air is perfectly still, traveling six miles an hour will 
cause a constant resistance of 3 lbs. on the carriage, or 
one fourteenth of the power exerted for a full day's 
work. The same speed against a " gentle wind" of six 
miles an hour, added, would increase the resistance four- 
fold, or equal to 12 lbs. ; more than one fourth of the 
horse's strength at six miles an hour through the day. 

WIND-MILLS. 

The power possessed by the sails of a wind-mill 
may be nearly ascertained in the same way, the area 
of the. sails being known, and first deducting their av- 
erage velocity. 

The force of wind may be usefully applied by al- 
most every farmer, as it is a universal agent, possess- 
ing in this respect great advantages over water-power, 
of which very few farms enjoy the privilege. 



224 



PNEUMATICS. 



Fig. 183. 





Wind may be applied to various purposes, such as 

sawing wood by the aid 
of a circular saw, turn- 
ing grindstones, and 
particularly in pumping 
water. One of the best 
contrivances for pump- 
ing is represented by 
Fig. 183, where A is 
the circular wind- mill, 
with a number of sails 
set obliquely to the di- 
rection of the wind, and 
always kept facing it 
by means of the vane, B. 
The crank of the wind- 
mill, during its revo- 
lutions, works the pump-rod, I, and raises the water 
from the well beneath. In whatever direction the wind 
may blow, the pump will continue working. The 
pump-rod, to work steadily, must be immediately un- 
der the iron rod on which the vane turns. If the di- 
ameter of the wind-mill is four feet, it will set the 
pump in motion even with a light breeze, and with a 
brisk wind will perform the labor of a man. Such a 
machine will pump the water needed by a large herd 
of cattle, and it may be placed on the top of a barn, 
with a covering, to which may be given the architec- 
tural effect of a tower or cupola, as shown in Fig. 184, 
opposite. 

A more compact machine, but of more complex con- 
struction, is shown in Fig. 185, opposite, where the up- 



Wind-mill for pumping water on farms : 
A, wind-mill ; B, vane ; I, pump-rod. 



WIND-MILLS. 
Fig. 184. 



225 




Barn surmounted with wind-mill for pumping water, 
cutting straw, tfC. 



Fig. 185. 




K2 



226 PNEUMATICS. 

per circle moves around with the wheel and vane on 
the fixed lower circle, to which it is strongly secured so 
as to admit of turning freely. In other respects it is 
similar to the preceding. 

In all wind-mills, it is important that the sails should 
have the right degree of inclination to the direction of 
the wind. If they were to remain motionless, the angle 
Would he different from that in practice. They should 
more nearly face the wind ; and as the ends of the sails 
sweep round through a greater distance and faster, they 
should present a natter surface than the parts nearer 
the centre. The sails should, therefore, have a twist 
given them, so that the parts nearest the centre may 
form an angle of ahout 68 degrees with the wind, the 
middle ahout 72 degrees, and the tips ahout 83 degrees. 

In order to produce the greatest effect, it is necessa- 
ry to give the sails a proper velocity as compared with 
the velocity of the wind. If they were entirely un- 
loaded, the extremities would move faster than the 
wind, in consequence of its action on the other parts. 
The most useful effect is produced when the ends move 
ahout as fast as the wind, or ahout two thirds the ve- 
locity of the average surface. 

The most useful wind is one that moves at the rate 
of eight to twenty miles per hour, or with an average 
pressure of ahout one pound on a square foot. In large 
wind-mills, the sails must he lessened when the wind 
is stronger than this, to prevent the arms from heing 
broken ; and if much stronger, it is unsafe to spread 
any, or to run them. 



CHIMNEY CURRENTS. 227 



CAUSES OF WIND. 



The motion of air in producing wind is explained by 
the action of heat, although there are many irregular 
currents whose cause is not well uuderstood. The 
simplest illustration of the effect of heat in causing cur- 
rents is furnished by the land and sea breezes in warm 
latitudes. The rays of the sun during the day heat the 
surface of the land, and the air in contact with it also 
becoming heated, and thus rendered lighter, flows up- 
ward ; the air from the sea rushes in to fill the vacancy 
and causes the sea-breeze. During the night, the ra- 
diation of heat from the land into the clear sky above 
cools the surface to a lower temperature than that of 
the sea ; consequently the air in contact with the sea 
becomes heated the most, and rising, causes the wind 
from the land to flow in and supply the place. Trade- 
winds are caused in a similar way, but on a much 
larger scale, by the greater heat of the earth at the 
equator, which produces currents from colder latitudes. 
These currents assume a westerly tendency, in conse- 
quence of the velocity of the earth being the greatest 
at the equator, and which, outstripping the momentum 
which the winds have acquired in other latitudes, tends 
to throw them behind, or in a westerly direction. 



SECTION II. 

CHIMNEY CURRENTS. 



Chimney Currents are produced by the heat of the 
fire rarefying the air, which rises and carries the smoke 
with it. The taller the chimney is, the longer will be 



228 



PNEUMATICS. 



the column of rarefied air tending upward, and, as a 
consequence, the stronger will be the draught. In kin- 
dling a fire in a cold chimney, there is very little cur- 
rent till this column becomes heated. The upward 
motion of heated currents is governed by laws similar 
to the downward motion of water in tubes, where the 
velocity is increased with the height of the head. But 
as air is more than eight hundred times lighter than 
water, slight causes will affect its currents, which would 
have no sensible influence on the motion of liquids. 
For instance, a strong wind striking the top of a chim- 
ney may send the smoke downward into the room ; 
and a current can not be induced through a horizontal 
pipe without connecting with it an upright pipe of con- 
siderable height. 



1 


Fig 


.is 


6. 










^ 


\\m^ § 



A well-built 
Chimney. 



CONSTRUCTION OF CHIMNEYS. 

In constructing chimneys to produce a 
strong draught, the throat immediately 
above the fire, which should have a breadth 
equal to that of the fire-place, should be 
contracted to a width of about four inches, 
so that the column of rising air above may 
draw the air up through the throat with 
increased velocity, as shown in Fig. 186. 
This arrangement also allows the fire to be 
built so as to throw the heat more fully out 
into the room. By leaving the shoulder 
at b square or flat, it will tend to arrest 
any reversed or downward cm-rent in a bet- 
ter manner than if built sloping, as shown 
by the dotted line at a, which would act 



CHIMNEY-CAPS. 



229 



Fig. 187. 



^V Ee 




like a funnel, and throw the smoke into the room. 
The throat should be about as high as the ex- 
treme tip of the flame ; if much higher, the 
chimney will not draw so well, and if lower, 
too much of the heat will be lost. Fig. 187 
shows a fire-place without a contracted throat, 
the current of which is comparatively feeble. 
Many chimneys draw badly by being made 
too large for the fire to heat sufficiently the 
column of air they contain. 

CHIMNEY-CAPS. 

"When wind sweeps over the roof of a high 
part of the building, or over a hill, it often 
strikes the top of chimneys below, and drives 
the smoke downward. This may be often 
prevented by placing a cap over the chim- 
ney, like that represented by Fig. 188, 
which is supported at its corners, the 
smoke passing out at the four sides just 
under the eaves of this cap. But it some- 
times happens that there is a confusion of 
currents and eddies at the top of the chim- 
ney, over which this cap has no influence. 
In this case, the cap represented by Fig. 
189 furnishes a perfect remedy, and is, in- 
deed, perfect in its operation under any cir- 
cumstances whatever, for the chimney sur- 
mounted by it will always draw when 
there is wind from any quarter, with or without any 
fire. It has effected a perfect cure in some chimneys 
which before were exceedingly troublesome, and were 



A badly-built 
Chimney. 

Fig. 188. 




Fig. 189. 




230 



PNEUMATICS. 




Fig. 190. regarded as incurable. Fig. 190 

is intended to show the mode of 
its operation, the wind, as shown 
by the arrows, being deflected for 
a considerable distance on the lee 
side, so as to form a vacancy at 
a, which the wind from the other end and from the 
chimney both rush in to supply. Being fixed on with- 
out turning in the chimney, it is both simpler and less 
noisy than any caps furnished with a vane. 

Emerson's Chimney-cap, lately invented, is differ- 
ent in construction, but quite similar in 
principle to the preceding. It is shown 
by Fig. 191. A sheet-iron pipe is set in 
the top of the chimney, furnished with 
the conical rim, and a plate or fender 
on the top which excludes the rain. Be- 
tween the plate and rim is a space 



Fig. 191. 




quite simi- 
lar in form or section to 
that represented by Fig. 
190. 

In exposed situations, 
chimneys are found to 
draw more uniformly by 
contracting the top about 
a third less than the rest 
of the flue. The current 
at the moment of escape 
is swifter than below, and 
less acted upon by any 
downward check from the 



Fig. 192. 




CHIMNEY-CAPS. 



231 



Fig. 193. 




wind, at the same time that the surface is 
smaller on which the wind can strike the 
current, as shown in Fig. 192. A chim- 
ney of this character may be very easily 
made by contracting the tiers of brick, thus 
giving to it an ornamental appearance, as 
seen in Fig. 193.* 



* Where different fires communicate with the same chimney, sep- 
arate flues should be built for each fire, and kept separate in the same 
chimney-stack, carried up independently of each other. But even 
with this precaution, smoky rooms will not be avoided, unless the ter- 
mination of the chimney is of the right form, of which the following 
illustration is given in Allen's Rural Architecture : 

" Fifteen years ago we purchased and removed into a most substan- 
tial and well-built stone house, the chimneys of which were construct- 
ed with open fireplaces, and the flues carried up separately to the top, 
where they all met upon the same level surface, as chimneys in past 
Fig. 194. times usually were built, thus. Every fireplace in 

the house (and some of them had stoves in) smoked 
intolerably ; so much so, that when the wind was in 
some quarters, the fires had to be put out in every 
room but the kitchen, which, as good luck would 
have it, smoked less — although it did smoke there — 
than the others. After balancing the matter in our 
own mind some time whether we would pull down and rebuild the 
chimneys altogether, or attempt an alteration — as we had given but lit- 
tle thought to the subject of chimney draft, and to try an experiment 
was the cheapest — we set to work a bricklayer, who, under our direc- 
tion, simply built over each discharge of the several flues a separate 
top of fifteen inches high, in this wise : the remedy 
was perfect. We have had no smoke in the house 
since, blow the wind as it may, on any and on all oc- 
casions. The chimneys can't smoke ; and the whole 
expense for four chimneys, with their twelve flues, 
was not twenty dollars ! The remedy was in giving 
each outlet a distinct current of air all around, and on 
every side of it." 





232 



PNEUMATICS. 



VENTILATION. 

Impure air may be breathed for a short time with- 
out any serious detriment, but to live in it and respire 
it for years can not fail to produce permanent injury to 
the health. During the heat of summer, open doors 
. and windows will usually furnish plenty of fresh air, 
as long as this season lasts, which in the Northern 
States is not one half of the year. During the rest of 
the time rooms are heated with close stoves, and unless 
special care is taken to secure fresh air, pale or sickly 
inmates will be the most likely results. 

Even with a common open fire-place, which causes 
more circulation of the air in a room than stoves, the 
ventilation is very imperfect. The following figure 
(Fig: 196) represents the fresh air as passing in from 

Fig. 196. 




A badly-ventilated Room. 

an open window opposite the fire, producing a direct 
current from the window to the chimney, and leaving 
all the upper portion of the room filled with bad air, 
unaffected by the change. The cold air can not rise, 
nor the hot air descend. This difficulty may be easily 



VENTILATION. 233 

removed by placing a register (which may he closed or 
opened at pleasure) at a, in the upper corner, so that 
the confined air may escape into the chimney. With- 
out this provision, it is nearly impossible to preserve 
the air in proper condition for breathing, for the upper 
part, being warmest and lightest, remains unchanged 
at the top. In rooms heated by stoves, registers for es- 
cape of the foul air are still more important, where the 
thermometer frequently indicates twenty degrees differ- 
ence in the heat above and at the floor, the lower stra- 
tum of air resting like a cold lake about the feet, while 
the head is heated unduly. 

"When the draught of the chimney-fire is not strong, 
the smoke may, however, escape through the ventilat- 
ing register into the room. To avoid this difficulty, it 
is best to provide separate air-flues in the walls when 
the house is built, for effecting perfect ventilation. In 
rooms strongly heated by fires, the fresh air should be 
admitted near the celling, producing descending cur- 
rents, and effecting a complete circulation in the air of 
the room. But in sleeping apartments and in closets, 
not heated artificially, and where the descending cur- 
rents will not take place, the fresh air should be admit- 
ted through a register or small rolling blind near the 
floor, and discharged near the ceiling into an air-flue. 
Fig. 197. The excessive warmth of 

garrets in mid-summer may be 
avoided by placing a ventilator 
at the highest part, and admit- 
ting air at windows or openings 
near the eaves (Fig. 197), thus 
Mode of ventilating Garrets, sweeping all the hot air out by 




234 



PNEUMATICS. 



the current produced ; or, the oppressive heat of half- 
story bedrooms may he similarly avoided, by creating 
a current of air between the roof and the plastering 
(Fig. 198). Two modes may be adopted, as repre- 
sented on each side of the figure. 

Fig. 198. 




Mode of Ventilating half-story Bed- 
rooms. 



PART IV. 

HEAT. 



CHAPTER I. 

CONDUCTION OF HEAT. 
SECTION I. 

CONDUCTING POWER OF BODIES. 

"When any substance or body has become heated, it 
loses its heat in two different ways, by conduction and 
by radiation. When conducted, heat passes off slow- 
ly or gradually through bodies, as when a pin is held 
by the hand in a candle, the heat advancing from one 
end to the other till it burns the fingers ; or, when an 
iron poker is thrust into the fire, the heat gradually 
passes through it till the whole becomes hot. Iron 
and brass are, therefore, said to be good conductors of 
heat. The end of a pipe-stem may, however, be heated 
to redness, and a wooden rod may be set on fire, with- 
out even warming the other extremity, because the 
heat is very slowly conducted through them. Wood 
and burned clay are, therefore, poor conductors. 

The comparative conducting power of different sub- 
stances may be shown by placing short rods of each 
with one of their ends in a vessel of hot sand, the oth- 
ers to be tipped with wax. The different periods of 
time required to melt the wax indicate the relative 






236 HEAT. 

conducting powers. It will speedily melt on the cop- 
per rod ; soon after, on the rod of iron ; glass will re- 
quire longer time ; stone or eathenware still longer ; 
while on a rod of wood it will scarcely melt at all. 
These rods should he laid horizontally, that the hot air 
rising from the sand may not affect the wax. The 
conducting powers may he judged of likewise, with 
considerable accuracy in cold weather, by merely plac- 
ing the hand upon the different substances. The best 
conductors will feel coldest, because they withdraw the 
heat most rapidly from the hand. Iron will feel colder 
than stone ; stone colder than brick ; wood still less so ; 
and feathers and down least of all, although the real 
temperature of all may be precisely the same. 

UTILITY OF THIS PRINCIPLE. 

A knowledge of this property is often very useful. 
For instance, it is found that hard and compact kinds 
of wood, as beach, maple, and ebony, conduct heat 
nearly twice as rapidly as light and porous sorts like 
pine and basswood. Hence doors and partitions made 
of light wood make a warmer house than those that are 
more heavy and compact. Pine or basswood would, 
in this respect, be better than oak or ash. 

Porous substances of all kinds are the poorest con- 
ductors ; saw-dust, for example, , being much less so 
than the wood that produced it. For this reason, saw- 
dust has been used as a coating around the boilers of 
locomotives to keep in the heat, and for the walls of 
ice-houses to exclude it. Sand, filled in between the 
double walls of a dwelling, renders it much warmer in 
winter and cooler in summer than if sandstone were 



CONDUCTING POWER OF LIQUIDS. 237 

made to fill the same space. Ashes, being more po- 
rous, are found to be still better. Tan, which is simi- 
lar to saw-dust, is well adapted to filling in the walls 
of stables and poultry -houses, where more than usual 
warmth in winter is required. Confined air is a very- 
poor conductor of heat ; hence the advantage of double 
walls and double windows, provided there are no crev- 
ices for the escape of the confined air. This principle 
has been lately applied in the manufacture of hollow 
brick for building the walls of dwellings. 

The fight and porous nature of snow renders it emi- 
nently serviceable as a clothing to the earth in the 
depth of winter, preventing the escape of the heat from 
below, and protecting the roots of plants from injury 
or destruction. Hence the very severity of the cold 
of the Northern regions, by producing an abundance of 
those beautiful feathery crystals which form snow, be- 
comes the means of protecting from its own effects the 
tender herbage buried beneath this ample shelter. 

CONDUCTING POWER OF LIQUIDS. 

Liquids are found to conduct heat very slowly, and 
they were for a long time considered perfect non-con- 
ductors. Some interesting experiments have been per- 
Fi g . 199. formed in illustration of this property. A 
large glass jar may be filled with water (Fig. 
199), in which may be fixed an air thermom- 
eter, which is always very quickly sensitive 
to small quantities of heat. A shallow cup 
of ether, floating just above the bulb, may be 
set on fire, and will continue to burn for 
some time before any effect can be seen upon 




238 HEAT. 

the thermometer. The upper surface of a vessel of wa- 
ter has been made to boil a long time, with a piece of 
unmelted ice at the bottom. Liquids are found, howev- 
er, to possess a conducting power in a very slight degree. 
When a vessel of water is heated in the ordinary- 
way over a fire, the heat is carried through it merely 
by the motion of its particles. The lower portion be- 
Fi 200 comes warm and expands ; it immediate- 
ly rises to the surface, and colder portions 
sink down and take its place, to ascend in 
their turn. In this way, a constant cir- 
culation is kept up among the particles. 
These rising and descending currents are 
shown by the arrows in Fig. 200. This 
result may be easily shown by filling a flask 
with water into which a quantity of saw- 
dust from some green hard wood has been 
thrown, which is about as heavy as water. 
It will traverse the vessel in a manner precisely like 
that shown in the figure. 

These results show the importance of applying heat 
directly to the bottom of all vessels in which water is 
intended to be heated. A considerable loss of heat oft- 
en occurs when the flame is made to strike against the 
sides only of badly-arranged boilers. 




SECTION II. 

EXPANSION BY HEAT. 

An important effect of heat is the expansion of bod- 
ies. Among many ways to show it, an iron rod may 
be so fitted that it will just enter a hole made for the 



EXPANSION BY HEAT. 



239 



purpose in a piece of sheet-iron. If the rod be now- 
heated in the fire, it expands and becomes larger, and 
can not be thrust into the hole. The expansion may- 
be more visibly shown and accurately measured by 
means of an instrument called the Pyrometer (Fig. 
201). The rod a b, secured to its place by a screw at 



Fig. 201. 




a, presses against the lever c, and this against the lever, 
or index, d, both of which multiply the motion, and 
render the expansion very obvious to the eye when the 
rod is heated by the lamps. If the rod should expand 
one fiftieth of an inch, and each lever multiplies twen- 
ty times, then the index (or second lever) will move 
along the scale eight inches ; for 20 times 20 are 400, 
and 400 50ths of an inch are 8 inches. 

Many cases showing the expansion of heated bodies 
occur in ordinary practice. One is afforded by the 
manner in which the parts of carriage wheels are bound 
together. The tire is made a little smaller than the 
wooden part of the wheel ; it is then heated till, by 



240 HEAT. 

expanding, it becomes large enough to be put on, when 
it is suddenly cooled with water, and by its powerful 
contraction binds every part of the wheel together with 
great force. Hogsheads are firmly hooped with iron 
bands in the same way, with more force than could be 
ever given by driving on with blows of the mallet. 

This principle was very ingeniously applied in draw- 
ing together two expanding brick walls of a large 
building in Paris, which threatened to burst and fall. 
Holes were drilled in the opposite walls, through which 
strong iron bars across the building projected, and cir- 
cular plates of iron were screwed on these projecting 
ends. The bars were then heated, which increased 
their length ; the plates were then screwed closely 
against the walls. On cooling, they contracted, and 
drew the walls nearer together. The process was re- 
peated on alternating bars, until the walls were re- 
stored to their perpendicular positions. 

All tools, where the wooden handles enter iron sock- 
ets, will hold more firmly if the metal is heated before 
inserting the wood. 

The metallic parts of pumps sometimes become very 
difficult to unscrew, and a case has occurred where 
two strong men could not start the screws, until a by- 
stander suggested that the outer piece be heated, keep- 
ing the inner cool, when a force of less than ten pounds 
quickly separated them. In other cases, where the 
large iron nuts have been thoughtlessly screwed, while 
warmed with the hands, on the cold metallic axles of 
wood-sawing machines in winter, they have contracted 
so that the force of two or three men has been insuffi- 
cient to turn them. 



THE STEAM-ENGINE. 



241 



The sudden expansion of bodies by heat sometimes 
causes accidents. • Thick glass vessels, when unequally 
heated, expand unequally, and break. Heated plates 
of cast iron or cast kettles are very liable to be frac- 
tured by suddenly pouring cold water upon them. The 
same effect has been usefully applied in splitting the 
scattered rocks which encumber a farm, and which 
are too large to remove while entire. Fires are built 
upon them ; the upper surface expands, while the low- 
er remains cold, and large portions are successively 
separated in scales, and sometimes the whole rock is 
severed. The only care needed is to observe atten- 
tively and remove with an iron bar any parts which 
may have become loosened by the heat, and which 
would prevent the heat from passing to other portions. 
One man will thus attend to a large number of fires, 
and will split in pieces ten times as many rocks in a 
day as by drilling and blasting. 




THE STEAM-ENGINE. 

The Steam-engine owes its power to 
the enormous expansion of water at the 
•moment it is converted into steam, which 
is about 1600 times its bulk when in the 
form of water. The principle on which 
the steam-engine acts may be understood 
by a very simple instrument represented 
in Fig. 202, A glass tube with a small 
bulb is furnished with a solid air-tight 
piston, capable of working up and down. 
The water in the bulb, a, is heated with 
a spirit-lamp or sand-bath ; the rising 



242 HEAT. 

steam forces up the piston. Now immerse the hulb in 
cold water or snow, and. the steam is condensed again 
into water, the tube is left vacant, and the pressure of 
the atmosphere forces down the piston. By thus al- 
ternately applying heat and cold, it is driven up and 
down like the piston of a steam-engine. The only dif- 
ference is, the steam-engine is furnished with appara- 
tus so that this application of heat and cold is perform- 
ed by the machine itself. The bulb represents the 
boiler, and the tube the cylinder ; but in the steam- 
engine the boiler is separate, and connected by a pipe 
with the cylinder ; and instead of applying the cold 
water directly to the cylinder, it is thrown into an- 
other vessel called the condenser, connected with the 
cylinder. 

When Newcomen, who made the first rude regular- 
ly-working engine, began to use it for pumping water, 
he employed a boy to turn a stop-cock, connected with 
the condenser, every time the piston made a stroke. 
The boy, however, soon grew tired of this incessant la- 
bor, and endeavored to find some contrivance for relief. 
This he effected by attaching a rod from the piston or 
working-beam to the cock, which was turned by the 
machine itself at every stroke. This was the origin 
of the first self-acting engine. 

The different parts of a common steam-engine may 
be understood from the following figures, one represent- 
ing the boiler, and the other the working machinery. 

The boiler, B (Fig. 203), contains water in the low- 
er part and steam in the upper ; F B is the fire ; v o is 
the feed-pipe ; v, a valve, closed by the lever, b c a, 
whenever the boiler is full enough, by means of the ris- 



THE STEAM-ENGINE. 



243 



ing of the float, S, and opened whenever the float sinks 
from low water. M, barometer gauge, to show the 



Fig. 203 




Boiler of Steam-engine. 

pressure of the steam ; w, weight on the lever, e b, for 
holding down the safety-valve : this lever heing grad- 
uated like a steelyard, the force of the steam may he 
accurately weighed. U. is a valve opening downward, 
to prevent the hoiler being ' crushed by atmospheric 
pressure, by allowing the air to pass in whenever the 
steam happens to decline. Two tubes with stop-cocks, 
c and d, one just below the water-level and the other 
just above it, serve to show, by opening the cocks, 
whether the water is too high or too low. 

The working part of the engine is represented in the 
figure on the following page {Fig. 204). The steam 
enters by the pipe, s, from the boiler on the other side 
of the brick wall, as shown in Fig. 203. The steam 



244 



HEAT. 




Low-pressure Steam-engine. 



passes through what is called & four-way-cock, a, first 
into the lower, then into the upper end of the cylinder, 
C, as the piston, P, moves up and down ; this is regu- 
lated by the levers, y y. The piston-rod, E, is attach- 
ed to the working-beam, B F, turning on the centre, A. 
The rod, F R, turns the fly-wheel, H H, and drives 
the mill, steam-boat, or machinery to be put in motion. 
The condenser, j, shown directly under the cylinder, 
remains to be described. It is immersed in a cistern 
of cold water, and is connected by pipes to the upper 
and lower end of the cylinder. Through these pipes 
the steam passes out of the cylinder, first from one end 
and then from the other, and is condensed into water 
by a jet of cold water thrown into it by the injection- 
cock. "When condensed, it is pumped out by the pump, 
0, into the well or reservoir, W, and then again into 



THE STEAM-ENGINE. 245 

the feed-pipe of the boiler. Warm water is thus con- 
stantly supplied to the boiler, and effects a great sav- 
ing of fuel. 

The supply of steam and the motion of the engine 
are regulated by the governor, Gr. "When the motion 
is too fast, the two suspended balls, which revolve on 
a vertical or upright axis, and which hang loosely like 
pendulums, are thrown out from the axis, producing 
the movement of a rod which shuts the steam-valve. 
When the motion is too slow, the balls approach the 
axis and open the valve. 

In high-pressure engines the steam is not condensed, 
but escapes into the open air at every stroke of the pis- 
ton, which produces the loud, successive puffs of all 
engines of this kind. 

. The steam-engine, in its most perfect form, is a 
striking example of human ingenuity, and its qualities 
are thus described by Dr. Arnott : " It regulates with 
perfect accuracy and uniformity the number of its 
strokes in a given time, and records them as a clock 
does the beats of its pendulum. It regulates the quan- 
tity of steam ; the briskness of the fire ; the supply of 
water to the boiler ; the supply of coals to the fire. It 
opens and shuts its valves with absolute precision as to 
time and manner ; it oils its joints ; it takes out any 
air accidentally entering parts which should be vacu- 
ous ; and when any thing goes wrong which it can not 
of itself rectify, it warns its attendants by ringing a 
bell ; yet, with all these qualities, and even when ex- 
erting a force of six hundred horses, it is obedient to 
the hand of a child. Its aliment is coal, wood, and 
other combustibles. It consumes none while idle. It 



246 HEAT. 

never tires, and wants no sleep. It is not subject to 
any malady when originally well made, and only re- 
fuses to work when worn out with age. It is equally 
active in all climates, and will do work of any kind : 
it is a water-pumper, a miner, a sailor, a cotton-spin- 
ner, a weaver, a blacksmith, a miller, a printer, and is 
indeed of all occupations ; and a small engine in the 
character of a steam pony may be seen dragging after 
it, on an iron rail- way, a hundred tons of merchandise 
or a thousand persons with the speed of the wind." 

Steam-engines have been much used on large farms 
in England for thrashing, grinding the feed of annuals, 
cutting fodder, and for other purposes. They have been 
less used here, but may prove useful for large estab- 
lishments, where the teams for ordinary tillage are in- 
sufficient for stationary labor. 

More difficulty exists in their use for plowing, in con- 
sequence of the labor and expense of moving frequent- 
ly so heavy a machine, and the still greater difficulty 
of using a locomotive power like that on rail-roads on 
the soft surfaces of farms. 

EXCEPTION TO EXPANSION BY HEAT. 

A striking exception to the general law of expansion 
by heat occurs in the freezing of water.* During its 
change to a solid state, it increases in bulk about one 
twelfth, and this expansion is accompanied with a 
great force. The bottoms of barrels are burst out, and 
cast-iron kettles are split asunder, when water is suf- 
fered wholly to freeze in them. Lead pipes filled with 

* There are a very few other substances which expand on passing 
from a liquid to a solid state. 



EXCEPTION TO EXPANSION BY HEAT. 247 

ice expand ; but if it is often repeated, they are crack- 
ed into fissures. A strong brass globe, the cavity of 
which was only one inch in diameter, was used by the 
Florentine academicians for the purpose of trying the 
expansive force of freezing water, by which it was 
burst, although the force required was calculated to be 
equal to fourteen tons. Experiments were tried at 
Quebec, in one of which an iron plug, nearly three 
pounds in weight, was thrown from a bomb-shell to 
the distance of 415 feet; and in another, the shell 
was burst by the freezing of the water which it con- 
tained. 

This expansion has a most important influence in 
the pulverization of soils. The water which exists 
through all their minute portions, by conversion to 
frost, crowds the particles asunder, and when thawing 
takes place, the whole mass is more completely mel- 
lowed than could possibly be effected by the most per- 
fect instrument. This mellowing is, however, of only 
short duration, if the ground has not been well drain- 
ed to prevent its becoming again packed hard by soak- 
ing with water. 

But this is not the most important result from the 
expansion of water. Much of the existing order of na- 
ture and of civilized life depends upon this property ; 
without it the great mass of our lakes and rivers would 
become converted into solid ice ; for, as soon as the 
surface became covered, it would sink to the bottom, 
beyond the reach of the summer's sun, and successive 
portions being thus added, the great body of all large 
rivers and lakes would become permanently frozen. 
But instead of this disastrous consequence, the ice, by 



248 HEAT. 

resting upon the surface, forms an effectual screen from 
the cold winds to the water "below. 



SECTION III. 

LATENT HEAT. 

If a vessel of snow, which has been cooled down to 
several degrees below freezing by exposure to the se- 
vere cold of winter, be placed over a steady fire with a 
thermometer in the snow, the mercury will rise by the 
increasing heat of the snow until it reaches the freez- 
ing point. At this moment it will stop rising, and the 
snow will begin to melt ; and although the heat is all 
the time passing rapidly into the snow, the thermom- 
eter will remain perfectly stationary till it is all con- 
verted to water. The heat that goes to melt the snow 
does not make it any hotter ; in other words, it becomes 
latent (the Latin word for hidden), so as neither to af- 
fect the sensation of the hand or to raise the thermom- 
eter. Now it has been found that the time required 
to melt the snow is sufficient to heat the same quantity 
of water, placed over the same fire, up to 172 degrees, 
or 140 degrees above freezing; that is, 140 degrees 
have become latent, or hidden, hi melting the snow. 

This same amount of heat may be given out again 
by placing the vessel of water out of doors to freeze. 
A thermometer will show that the water is growing 
colder by the escape of the heat, till freezing commen- 
ces. After this it still continues to pass off, but the 
water becomes no colder till all is frozen, as it was 
only the latent heat of the water that was escaping. 

A simple and familiar experiment exhibits the same 



LATENT HEAT OF STEAM. 249 

principle. Place a frozen apple, which thaws a little 
below freezing, in a vessel of ice-cold water. The la- 
tent heat of the water immediately passes into the 
apple and thaws it, and in an hour or two it will be 
found like a fresh apple and entirely free from frost; 
but the latent heat having escaped from the water 
next the apple, a thick crust of ice is found to en- 
case it. 

The amount of latent heat may be shown in still 
another way. Mix a pound of snow at 32 degrees, or 
at freezing, with a pound of water at 172 degrees. 
All will be melted, but the two pounds of water thus 
formed will be as cold as the snow, showing that for 
melting it the 140 degrees in the hot water were all 
made latent. 

ADVANTAGES OF LATENT HEAT. 

If no heat became latent by the conversion of ice 
and snow to water, no time would, of course, be required 
for the process, and thawing would be instantaneous. 
On the approach of warm weather, or at the very mo- 
ment that the temperature of the air rose above freez- 
ing, snow and ice would all dissolve to water, and ter- 
rific floods and inundations would be the immediate 
consequence. 

LATENT HEAT OF STEAM. 

A still larger amount of latent heat is required for 
the conversion of water into steam ; for, again place 
the vessel of water with its thermometer on the fire, 
it will rise, as the heat of the water increases, to 212 
degrees, and then commence boiling. During all this 
L2 



250 HEAT. 

time it will now remain stationary at 212, till the wa- 
ter is all boiled away. This is found to require nearly 
five times the period needed to heat from freezing to 
hoiling ; that is, nearly one thousand degrees of heat 
are made latent by the conversion of water into 
steam. 

When the steam is condensed again to water, this 
heat is given out. Hence the use made of steam con- 
veyed in pipes for heating buildings, and for boiling 
large vats or tubs of water, by setting free this large 
amount of latent heat which the fire has imparted to it. 

GREEN AND DRY WOOD FOR FUEL. 

A great loss is often sustained -in burning green 
wood for fuel, from an ignorance of the vast amount 
of latent heat consumed to drive off the water the 
wood contains. "When perfectly green, it loses about 
one third of its weight by thorough seasoning, which 
is equal to about 25 cubic feet in every compact cord, 
or 156 imperial gallons. Now all this water must be 
evaporated before the wood is burned. The heat thus 
made latent and lost, being five times as great as to 
heat the water to boiling, is equal to enough for boiling 
780 imperial gallons in burning up every cord of green 
wood. The farmer, therefore, who burns 25 green 
cords in a winter, loses heat enough to boil more than 
fifteen thousand gallons of water, which would be 
saved if his wood had been previously well seasoned 
under shelter. 

The loss in using green fuel is, however, sometimes 
overrated. It has been found by experiment that one 
pound of the best seasoned wood is sufficient to heat 



GREEN AND DRY WOOD FOR FUEL. 251 

27 lbs. of water from the freezing to the "boiling point* 
This will he equal to heating and evaporating four 
pounds of water by every pound of wood. The 25 
cubic feet of water, therefore, in every cord of green 
wood, weighing about 1500 pounds, would require near- 
ly 400 pounds of wood for its evaporation, or about one 
seventh or one eighth of a cord. Hence we may infer 
that seven cords of dry wood are about equal to eight 
cords of green. This imperfect estimate will apply 
only to the best hard wood, and will vary exceedingly 
with the different sorts of fuel ; the more porous the 
wood becomes, the greater will be the necessity for 
thorough seasoning. 

Superficial observation often leads to very erroneous 
conclusions. Seasoned wood will sometimes burn with 
great rapidity, and, producing an intense heat for a 
short time, will favor an over-estimate of its superior- 
ity, (xreen wood, on the other hand, kindles with dif- 
ficulty, and burns slowly and for a long time ; hence, 
where the draught of the chimney can not be control- 
led, it may be the most economical, because a less pro- 
portion of heat may be swept upward than by the more 

* The following results show the heating power of several combust- 
ibles : 

1 lb. of wood (seasoned, but still holding 20 per cent, of water) 

raised from 32° to 212° 27 lbs. water. 

1 lb. of alcohol 68 " " 

1 lb. of charcoal 78 " " 

1 lb. of oil or wax 90 " . " 

1 lb. of hydrogen 216 " " 

It should be remembered that by ordinary modes of heating water, 
a very large proportion of the heat is wasted by passing up the chim- 
ney and into surrounding bodies, and the air. 



252 HEAT. 

violent draught produced from dry materials. Where 
the draught can be perfectly regulated, however, seas- 
oned wood should be always used, both for convenience 
and comfort, and for economy. 

Where wood is to be drawn to a distance, the pre- 
ceding estimate shows that the conveyance of more 
than half a ton of water is avoided in every cord by 
seasoning. 



RADIATION OF HEAT. 253 



CHAPTER II. 

RADIATION OF HEAT. 

The passage of heat through conducting bodies has 
been already explained. There is another way in 
which it is transmitted, termed radiation, in which it 
is thrown off instantaneously in straight lines from 
hot bodies, in the same way that light is thrown off 
from a candle. A familiar instance is furnished by 
the common or open fire-place, before which the face 
may be roasted with the radiated heat, while the back 
is chilled with cold. A screen held in the hand will 
intercept this radiated heat, showing that it flies in 
right lines like the rays of light. 

Radiated heat is reflected by a polished metallic 
surface, in the same way that light is reflected by a 
looking-glass. A plate of bright tin held near the fire 
will not for a long time become hot, the heat being 
reflected from it without entering and heating it. But 
if it be blackened with smoke, it will no longer reflect, 
but absorb the heat, and consequently will speedily 
become hot. This experiment may be easily tried by 
placing a new tin cup containing water over a char- 
coal fire, which yields no smoke. The heat will be 
reflected into the fire by the tin, and the water will 
scarcely become warm. But if a few pine shavings 
be thrown on this fire to smoke the surface of the tin, 
it will then absorb the heat rapidly, and soon begin to 
boil. This explains the reason that bread bakes more 



254 



HEAT. 



slowly in a new tin dish, and that a polished andiron 
before a fire is long in becoming hot. 

A concave burning-mirror, which throws the rays of 
heat to a focus or point, may be made of sheet-tin, by 
beating it out concave so as to fit a regularly curved 
gauge. If a foot in diameter, and carefully made, it 
will condense the rays of heat so powerfully at the fo- 
cus, when held several feet from the fire, as to set fire 
to a pine stick or to flash gunpowder (Fig. 205). 

Fig. 205. 




The reflection of radiated heat may be beautiful- 
ly exhibited by using two such concave tin mirrors. 
Place them on a long table several feet apart, and as- 
certain the focus of each by means of the light of a 
candle. Then place in the focus of one a red-hot iron 
ball, or a small chafing-dish of burning charcoal. In 
the focus of the other place the wick of a candle with 
a small shaving of phosphorus in it. The heat will 
be reflected, as shown by the dotted lines (Fig. 206), 

Fig. 206. 




DEW AND FROST. 255 

and, setting fire to the phosphorus, will light the 
candle. 

If a thermometer be placed in the focus of one mir- 
ror while the hot iron ball is in the other focus, it will 
rise rapidly ; but if a lump of ice be substituted for 
the ball, the thermometer will immediately sink, and 
will continue to do so until several degrees lower than 
the surrounding air ; because the thermometer radi- 
ates more heat to the mirrors, and then to the ice, than 
the ice returns. 

DEW AND FROST. 

All bodies are constantly radiating some heat, and 
if an equal amount is not returned by others, they 
grow colder, like the thermometer before the lump of 
ice. Hence the reason that on clear, frosty nights, ob- 
jects at the surface of the earth become colder than 
the air that surrounds them. The heat is radiated 
into the clear space above without being returned ; 
plants, stones, and the soil thus become cooled down 
below freezing, and, coming in contact with the moist- 
ure of the air, it condenses on them and forms dew, or 
freezes into ivhite frost. Clouds return or prevent the 
passage of the heat that is radiated, which is the rea- 
son there are no night-frosts in cloudy weather. A 
very thin covering, by intercepting the radiated heat, 
will often prevent serious injury to tender plants. 
Even a sheet of thin muslin, stretched on pegs over 
garden vegetables, has afforded sufficient protection, 
when those around were destroyed. 



256 HEAT. 

FROST IN VALLEYS. 

On hills, where the wind blows freely, it tends to 
restore to plants the heat lost by radiation, which is 
the reason that hills are not so liable to sharp frosts as 
still valleys. When the air is cooled it becomes heav- 
ier, and, rolling down the sides of valleys, forms a lake 
of cold air at the bottom ; this adds to the liability of 
frosts in low places. The coldness is frequently still 
further increased by the dark and porous nature of the 
soil in low places radiating heat faster to the clear sky 
than the more compact upland soil. 

A knowledge of these properties teaches us the im- 
portance of selecting elevated places for fruit-trees, and 
all crops liable to be cut off by frost ; and it also explains 
the reason that the muck or peat of drained swamps is 
more subject to frosts than other land on the same lev- 
el. Therefore, corn and other tender crops upon such 
porous soils must be of the earliest ripening kinds, so 
as to escape the frosts of spring by late planting, and 
those of autumn by early maturity. 

REMARKABLE EFFECTS OF HEAT ON WATER. 

The effects of heat and cold on water are of a very 
interesting character. "Without its expansion in freez- 
ing, the soil would not be pulverized by the frost of 
winter, but would be found hard, compact, and diffi- 
cult to cultivate in spring ; without its expansion into 
steam, the cities which are now springing up, and the 
continents that are becoming peopled, through the in- 
fluence of rail- ways, steam-ships, and steam manufac- 
tures, would mostly remain unbroken forests ; without 



REMARKABLE EFFECTS OF HEAT ON WATER. 257 

the crystallization of water, the beautiful protection of 
plants by a mantle of snow, in northern regions, would 
give place to frozen sterility ; without the conversion 
of heat to a latent state in melting, the deepest snows 
would disappear in a moment from the earth, and 
cause disastrous floods ; without its conversion to a la- 
tent state in steam, the largest vessel of boiling water 
would instantly flash into vapor. All these facts show 
that an extraordinary wisdom and forethought planned 
these laws at the creation ; and even what aopears at 
first glance as an almost accidental exception in the 
contraction of bodies by cold, and which causes ice to 
float upon water, preventing the entire masses of riv- 
ers and lakes from becoming permanently frozen, fur- 
nishes one out of an innumerable array of proofs of 
creative design in fitting the earth for the comfort and 
sustenance of its inhabitants. 



APPENDIX. 



APPARATUS FOR EXPERIMENTS. 

For the assistance of lecturers, teachers, and home students, the fol- 
lowing list is given of cheap and simple apparatus and materials for 
performing most of the experiments described in this work. These 
experiments, although simple, exhibit principles of much practical im- 
portance. A few articles of a more costly character are given in a 
second list. 

1. Inertia apparatus, p. 23. The concave post or stand is sufficient, 
the snapping being done by the finger, although a spring-snap performs 
the experiment more perfectly. 

2. Weight with two hooks and fine thread, p. 23. 

3. The inertia of falling bodies may be simply shown, and the pile- 
engine illustrated, by placing a large wooden peg or rod upright in a 
box of sand, and then dropping a weight upon its head at different 
heights, which will drive the rod into the sand more or less, according 
to the distance passed through by the falling weight. 

4. A straw-cutter, so made that the fly-wheel can be easily taken off, 
will show in a very striking manner the efficacy of this regulator of 
force. 

5. Two lead musket balls will exhibit the experiment in cohesion, 
p. 42. Balls or lead weights with hooks may be separated by sus- 
pending weights to show the amount of force required to draw them 
asunder. Metallic buttons or plates an inch in diameter, with hooks, 
will show the great strength needed to separate them when coated 
with grease, p. 42. 

6. Capillary tubes of different sizes, two straight small panes of glass, 
and a vessel of water, highly colored with cochineal or other dye, to 
exhibit capillary attraction. 

7. Glass tube, piece of bladder, and alcohol, for experiment described 
on p. 49. 

8. The cylinder for rolling up the inclined plane, represented by 



260 APPENDIX. 

Fig. 18, p. 50, may be very easily made by using a round pasteboard 
box a few inches in diameter, and securing a piece of lead inside by 
loops made with a needle and thread. The object shown by Fig. 19 
may be cut in one piece out of a pine shingle, the centre rod being 
lengthwise with the grain ; the two extremities are shaved small, and 
wound with thick sheet-lead, and the whole then colored or painted a 
dark hue, to render the lead inconspicuous. The experiment with the 
penknives, p. 51, is very simple, care being taken to insert them low 
enough in the stick. 

9. Irregular pieces of board, variously perforated with holes, and 
furnished with loops to hang on a pin, may be used to determine the 
centre of gravity, according to the principle explained by Fig. 21, p. 51. 

10. Portions of plank and blocks of wood, with the centre of gravity 
determined as in the last experiment, may have a plumb-line (which 
may be a thread and small perforated coin) attached to this centre, and 
then be placed on differently inclined surfaces, to show their upsetting 
just as this line of direction falls without the base. Toy-wagons, 
bought at the toy-shops, may be variously loaded and used in experi- 
ments of this sort. 

11. Experiments with the lever of the first kind may be easily per- 
formed by the use of a flat wooden bar, two or three feet in length, 
marked into inches, and placed on a small three-cornered block as a 
fulcrum. Weights, such as are used for scales, may be variously 
placed upon the lever. Levers of the second and third kind, which 
are lifted instead of borne down, may have a cord attached to the point 
where the power is to be applied, running up over a pulley or wheel, 
with a weight suspended to the other end. 

12. An axle, furnished with wooden wheels with grooved edges, of 
different sizes, may be used to exhibit the principle of the wheel and 
axle, in connection with scale-weights that are furnished with hooks. 
The power of combined cog-wheels may be shown by a combination 
like that represented on p. 76, using weights for both cords. 

13. Interesting experiments with the inclined plane, at different de- 
grees of slope, by a contrivance similar to that represented by Fig. 87, 
p. 104, with the addition of a small wheel at the upper side for a cord 
to pass over. This cord is fastened at one end to a light toy-wagon, 
running up and down the plane, and at the other to a weight suspend- 
ed perpendicularly just beyond the upper edge of the plane. The 
wagon is variously loaded with weights to counterpoise the suspended 
weight at different degrees of inclination. 



APPENDIX. 261 

14. A lecturer may quickly demonstrate before a class the small in- 
crease in the length of a road, in consequence of a considerable curve 
to one side of a straight line (as shown by Fig. 70), by using a cord 
for measuring, the diagram being marked on a board or the wall. 

15. A round stick of wood, and a long, wedge-shaped slip of paper, 
easily show the principle of Fig. 75, p. 94. 

16. A cog-wheel with endless screw and winch, Fig. 77, p. 95, ex- 
hibits distinctly the great power of the screw in this combination. 

17. Pine sticks, two feet long, and one fourth to one half inch 
through, of different shapes and sizes, supported at each end, and with 
weights hung at the middle till they break, may be made to illustrate 
the principles described on p. 100, 102. 

18. Some of the principles of draught maybe shown, and especially 
those in relation to the different angles of inclination for hard and soft 
roads, by using a common spring-balance as a dynamometer, attached 
to a hand-wagon, and also to a sliding block of wood. 

19. Bent glass tubes, with arms of different sizes to indicate the up- 
ward pressure of liquids, may be procured cheaply at glass-works. The 
experiment described by Fig. 154, p. 182, may be rendered easy and 
interesting by purchasing a large and perfectly-working syringe, and 
attaching to its nose, by means of sealing wax, a slender glass tube 
two or three feet long. Fill the syringe with water, leaving the 
tube empty ; then, with the tube upright, drive the water up through 
it with the piston of the syringe, and the increased weight felt on the 
piston as the column of water rises will be very evident. 

20. A hydrostatic bellows a foot in diameter, made by any good 
mechanic, will answer the purpose well, and exhibit an important 
principle. 

21. Specific gravities may be shown before a class by a common 
balance and a fine cotton or silk thread. 

22. A tin pail, with a hole half an inch or an inch in diameter at the 
bottom, will show the contracted stream which pours from it, p. 191. 
A short tin tube, with a slight flange at the upper end (quickly made 
by any tin-worker), fitted into this hole, will increase the discharge, as 
shown by Figs. 159, 160, and the difference in time for emptying the 
vessel may be measured by a stop-watch. 

23. Archimedes' screw is readily made by winding a lead pipe round 
a wooden cylinder. 

24. A glass syphon, filled with cochineal water, shows distinctly the 
theory of waves, by blowing with the mouth into one end. 



262 



APPKNDIX. 



25. Any vessel, filled with sand which has been heated over a fire, 
with rods of different substances, nearly of an equal size and length, 
and thrust with one end into the hot sand, in an inclined or nearly 
horizontal position, will exhibit the various conducting powers of these 
rods by melting pieces of wax or tallow placed on the ends most re- 
mote from the sand. 

26. The expansion by heat may be demonstrated by fitting an iron 
rod to a hole in sheet iron ; on heating the bar, it can not be made to 
enter. Or, if a hot iron ring be slipped on a tapering cold iron rod, it 
will contract on cooling so that the force of a man can not withdraw 
the rod. 

27. The rising and descending currents in a vessel of heating water 
are easily rendered visible by throwing into a glass vessel, or flask, 
over a lamp, particles of sawdust from any hard green wood, whose 
specific gravity is about the same as that of water. 

28. Instrument figured on p. 241, for showing the principle of the 
steam-engine. 

29. Experiments in latent heat may be easily exhibited with the as- 
sistance of a common thermometer. 

30. Tin mirrors for showing radiation, p. 254. 

Second List, containing a few of the more costly pieces of appara- 
tus for experiments as described in this treatise. 

1. A good compound or solar microscope will exhibit the minute 
animalcules described under the head of Divisibility. The larger of 
these animalcules may be seen in old strong vinegar, and the smaller 
in a drop of water taken from a vessel in which a portion of raw po- 
tato has been soaked a few hours in a warm place. The same instru- 
ment will show the pores of wood mentioned under the head Impene- 
trability. 

2. Atwood's machine, p. 39. 

3. A good dynamometer for field experiments is of great value and 
importance. 

4. An air-pump, with the several pieces of apparatus connected with 
it, shows, in an interesting and striking manner, several important 
principles. 



APPENDIX. 



263 



HYDROSTATICS AND HYDRAULICS. 

TABLE OF SPECIFIC GRAVITIES. 

Metals. 

Gold, pure 19.36 

" standard 17.16 

Mercury 13.58 

Lead 11.35 

Silver 10.50 

Copper .■ . 8.82 



Iron 7.78 

" cast 7.20 

Steel 7.82 

Brass, common 7.82 

Tin 7.29 

Zinc 6.86 



Stones and Earths. 



Brick 1.90 

Chalk 2.25 to 2.66 

Clay 1.93 

Coal, anthracite, about. . .1.53 

Coal, bituminous 1.27 

Charcoal 44 

Earth, loose, about 1.50 

Flint 2.58 

Granite, about 2.65 



Gypsum 1.87 to 2.17 

Limestone 2.38 to 3.17 

Lime, quick 80 

Marble 2.56 to 2.69 

Peat 60 to 1.32 

Salt, common 2.13 

Sand 1.80 

Slate 2.67 



Woods — dry. 
Green wood often loses one third of its weight by seasoning, and 
sometimes more. The same kind varies in compactness with soil, 
growth, exposure, and age of the trees. 



Apple 68 to .79 

Ash, white 72 to .84 

Beech 72 to .85 

Box 91 to 1.32 

Cherry 71 

Cork 24 

Elm 58 to .67 

Hickory 84 to 1.00 

Maple 65 to .75 

Pine, white 47 to .56 



Pine, yellow 55 to .66 

Oak, English 93 to 1.17 

" white 85 

" live 94 to 1.12 

Poplar, Lombardy .40 

Pear 66 

Plum 78 

Sassafras 48 

Walnut 67 

Willow 58 



264 APPENDIX. 



Miscellaneous. 



Beeswax 96 

Butter 94 

Honey 1.45 

Lard 94 

Milk 1.03 

Oil, linseed 94 



Oil, whale 92 

" turpentine 87 

Sea water 1.02 

Sugar 1.60 

Tallow. 93 

Vinegar 1.01 to 1.08 



Weights of a Cubic Foot of various Substa?ices, from ivhich the Bulk of 
a Load of one Ton may be easily calculated. 

Cast Iron 450 pounds. 

Water 62 " 

White pine, seasoned, about 30 " 

White oak, " " f 52 " 

Loose earth, about 95 " 

Common soil, compact, about 124 " 

Clay, about ..... 135 " 

Clay with stones, about 160 " 

Brick, about 125 " 

Bulk of a Ton of different Substances. 
23 cubic feet of sand, 18 cubic feet of earth, or 17 cubic feet of clay, 
make a ton. 18 cubic feet of gravel or earth before digging, make 27 
cubic feet when dug ; or the bulk is increased as three to two. There- 
fore, in filling a drain two feet deep above the tile or stones, the earth 
should be heaped up a foot above the surface, to settle even with it, 
when the earth is shoveled loosely in. 



DISCHARGE OF WATER THROUGH PIPES. 
Table showing the amount of water discharged per minute through 
an orifice one inch in diameter ; also through a tube one inch in di- 
ameter and two inches long, according to experiment. To ascertain 
the amount in gallons, divide the cubic inches by 231. 



APPENDIX. 



265 



Height of head 
of Water. 



Amount discharged 
through Orifice. 



1 Paris foot* 2,722 cub. in. 



2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 



3,846 
4,710 
5,436 
6,075 
6,654 
7,183 
7,672 
8,135 
8,574 
8,990 
9,384 
9,764 
10,130 
10,472 



Amount discharged 
through Tube. 

3,539 cub. in. 

5,002 

6,126 

7,070 

7,900 

8,654 

9,340 

9,975 
10,579 
11,151 
11,693 
12,205 
12,699 
13,177 
13,620 



VELOCITY OF WATER IN PIPES. 
The following table shows the height of a head of water required to 
overcome the friction in horizontal pipes 100 feet long, and to produce 
a certain velocity, according to Smeaton : 



Bore of 

Pipes. 6 Inches 
in. in. 

1 4.5 


1/oot. 
16.7 


Hfeet. 

in. 

35.1 


2feet. 
ft. in. 

4 9.7 


Zfeet. 

ft. in. 

10 1.0 


4feet. 

ft. in. 

17 10.0 


bfeet. 
ft. in. 

28 0.2 


i 


3.0 


11.1 


23.3 


3 


2.5 


6 


8.6 


11 


10.6 


18 8.1 


1 


2.2 


8.4 


17.5 


2 


4.9 


5 


0.5 


8 


11.0 


14 0.0 


1* 


1.8 


6.7 


14.0 


1 


11.1 


4 


0.4 


7 


1.6 


11 2.5 


11 


1.5 


5.6 


11.7 


1 


7.2 


3 


4.3 


5 


11.3 


9 4.1 


If 


1.3 


4.8 


10.0 


1 


4.5 


2 


10.6 


5 


1.1 


8 0.1 


2 


1.1 


4.2 


8.7 


1 


2.4 


2 


6.2 


4 


5.5 


7 0.0 


2i 


1.0 


3.7 


7.8 


1 


0.8 


2 


9.9 


3 


11.6 


6 2.7 


21 


0.9 


3.3 


7.0 





11.5 


2 


0.2 


3 


6.8 


5 7.2 


3 


0.7 


2.8 


5.0 





9.6 


1 


8.2 


2 


11.7 


4 8.0 


31 


0.6 


2.4 


5.0 





8.2 


1 


5.3 


2 


6.6 


4 0.0 


4 


0.6 


2.1 


4.4 





7.2 


1 


3.1 


2 


2.7 


3 6.0 



Look for the velocity of the water per second in the pipe, in the up- 
per line ; and in the column beneath it, and opposite the given diam- 

* A Paris foot is about 12 4-5 U. S. inches, and 15 Paris feet are about 16 TJ. S. feet. 

M 



2m 



APPENDIX. 



cter of the pipe, is the height of the column or head required to obtain 
the required velocity. 

To find the quantity of water discharged each minute, multiply the 
velocity by 12, which will give the inches per second ; then multiply 
this product by 60, which will give the inches per minute ; then, to 
change these cylindrical inches into cubic inches, multiply by 4 and 
divide by 5.* Divide the cubic inches by 231, and the result will be 
gallons. 

By comparing this table with the next preceding, we shall perceive 
that the water flows from three to four times as fast through the tube 
two inches long, as through a tube one hundred feet long, the diameter 
of the tube and the head of water being the same. 



RULE FOR THE DISCHARGE OF WATER. 
The following general formula, or rule applicable to different cases, 
has been furnished by a practical engineer. It may be useful in ascer- 
taining the quantity required to fill the driving pipe of a water-ram, and 
for various other purposes occasionally occurring in practice. 




Let A represent the fountain or reservoir from which water is to be 
conveyed to the trough B through the pipe L. Let N be the height 
of the surface of the water in the reservoir, above the place of dis- 
charge, and let D be the diameter of the tube in the smallest part. It 
is required to find the quantity Q which will be discharged in a second 
of time. The length and height being given in feet, and the diameter 
of the tube in inches, the formula, when the quantity is required in 
gallons, is as follows : 

Q = 0.608 -/(D 5 ^). 

* This gives the cubic inches very nearly ; but, to be more accurate, multiply by 
the decimal .7854, which represents the difference between the area of a square and 
of a circle. 



APPENDIX. 267 

In order to make the above formula more intelligible : 

Let L = 80 rods or 1320 feet. 

« H = 50 feet. 

" D = 2 inches. 

" Q = gallons. 

50 \ 
Then Q = 0.608^(32 X^j =0.67 ; or, the same may be thus 

expressed in words. 

Divide the height (50) by the length (1320) ; multiply the quotient 
by the fifth power of the diameter (fifth power of 2 = 32) ; extract the 
square root of the product, which, being multiplied by 0.608, will give 
(0.67) the number of gallons the tube will discharge in one second ; 
which in this case is 40 gallons in one minute. 



THE END. 



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